Future nuisance flooding at Boston caused by astronomical tides alone
2016; American Geophysical Union; Volume: 4; Issue: 12 Linguagem: Inglês
10.1002/2016ef000423
ISSN2328-4277
Autores Tópico(s)Coastal and Marine Dynamics
ResumoEarth's FutureVolume 4, Issue 12 p. 578-587 Research ArticleOpen Access Future nuisance flooding at Boston caused by astronomical tides alone Richard D. Ray, Corresponding Author Richard D. Ray richard.ray@nasa.gov Laboratory for Geodesy & Geophysics, NASA Goddard Space Flight Center, Greenbelt, Maryland, USACorresponding author: R. D. Ray, richard.ray@nasa.govSearch for more papers by this authorGrant Foster, Grant Foster Tempo Analytics, Garland, Maine, USASearch for more papers by this author Richard D. Ray, Corresponding Author Richard D. Ray richard.ray@nasa.gov Laboratory for Geodesy & Geophysics, NASA Goddard Space Flight Center, Greenbelt, Maryland, USACorresponding author: R. D. Ray, richard.ray@nasa.govSearch for more papers by this authorGrant Foster, Grant Foster Tempo Analytics, Garland, Maine, USASearch for more papers by this author First published: 25 October 2016 https://doi.org/10.1002/2016EF000423Citations: 63AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract Sea level rise necessarily triggers more occurrences of minor, or nuisance, flooding events along coastlines, a fact well documented in recent studies. At some locations nuisance flooding can be brought about merely by high spring tides, independent of storms, winds, or other atmospheric conditions. Analysis of observed water levels at Boston indicates that tidal flooding began to occur there in 2011 and will become more frequent in subsequent years. A compilation of all predicted nuisance-flooding events, induced by astronomical tides alone, is presented through year 2050. The accuracy of the tide prediction is improved when several unusual properties of Gulf of Maine tides, including secular changes, are properly accounted for. Future mean sea-level rise at Boston cannot be predicted with comparable confidence, so two very different climate scenarios are adopted; both predict a large increase in the frequency and the magnitude of tidal flooding events. Key Points Continuing sea level rise can induce coastal flooding from tides alone, without help from storms or other meteorological conditions Tide-induced nuisance flooding began to occur in Boston in 2011 and will become more prevalent Tide prediction at Boston must account for secular trend in tides and an unusual nodal modulation 1 Introduction As global sea levels rise, the number and severity of coastal flooding events increase. A large literature now exists which examines various aspects of coastal flooding and its dependence on mean sea level (MSL) rise, often couched in terms of exceedance probabilities and mean recurrence times for defined flood levels—see, for example, work by Church et al. [2006]; Purvis et al. [2008]; Lewis et al. [2011]; Weiss et al. [2011]; Tebaldi et al. [2012]; Ezer and Atkinson [2014]; Sweet and Park [2014]; Kriebel et al. [2015]. For Boston specifically, see Kirshen et al. [2008]; Kruel [2016]. It is generally recognized that the major societal impact of sea-level change occurs from extreme events such as those associated with severe storms. Yet as seas rise it is also possible that flooding starts occurring at fairly normal high tides, with no additional assistance from atmospheric pressures, winds, or rain. These tidal flooding events are “nuisance” floods, not normally catastrophic by themselves, but they are still capable of affecting large populations in low-lying coastal areas by making roads impassable, by infiltrating waste-water systems and other structures, and by necessitating occasionally costly clean ups. Tidally induced nuisance flooding is becoming more common [Ezer and Atkinson, 2014; Spanger-Siegfried et al., 2014; Moftakhari et al., 2015]. The present paper looks in detail at one such case, for the major metropolitan city of Boston, and tabulates all expected future cases through year 2050 of nuisance flooding induced strictly by tides acting alone. A recent spectral analysis of Boston tide-gauge data by one of us (see http://tamino.wordpress.com/2015/11/04/moon-over-miami-boston) suggests that “tide only” nuisance flooding first began occurring in Boston in 2011. Those results are here confirmed with more traditional tidal analysis and prediction calculations, although augmented in several ways. Such calculations can be employed to predict flooding events in coming decades. Obviously, meteorological conditions, which cannot be predicted with comparable precision, could act to mitigate or worsen any predicted tidal-flooding event, in exactly the same way that meteorological conditions can always affect a tidal prediction. Nonetheless, knowing of such predicted events, and understanding how they are changing over time, is of both scientific and societal interest. By way of comparison, the report by Spanger-Siegfried et al. [2014] is a comprehensive assessment at 59 tide gauges, including Boston, for which expected future nuisance flooding is estimated. Their projections are based on a statistical compilation of cases of actual flooding at each gauge over the 2009–2013 interval, which is then projected into the future based on an adopted sea-level rise scenario at that gauge. In contrast, this paper explicitly determines all future nuisance flooding events by tidal prediction combined with a sea-level rise scenario, and it thus allows tabulation of actual expected events. The former approach will include events not caused by tides acting alone, and only in a statistical sense, whereas the latter approach will include actual events, but ones that subsequent atmospheric conditions could conceivably either mitigate or worsen. Boston sits in the lower Gulf of Maine. Throughout the entire gulf the tides are large, remarkably so to the north of Boston and into the Bay of Fundy. The amplitude of the principal semidiurnal constituent M2 at Boston is approximately 137 cm. The Gulf of Maine tides also have some peculiar properties that make accurate tidal prediction over long periods somewhat more complicated than usual, and standard prediction algorithms must be modified to reflect this. One complication is a secular trend in tidal harmonic constants, present at Boston although even larger at ports to the north such as Eastport, Maine [Ray, 2006]. These matters are addressed in Section 3. The main results for expected tidal flooding are given in Section 4. 2 Sea Level Setting at Boston The tide gauge, established in May 1921, sits adjacent to the Northern Avenue Bridge, at latitude 42°21.3′N, longitude 71°3.2′W. Originally consisting of a standard float/well system, the gauge was upgraded in 1993 to an Aquatrak acoustic system. The fundamental sea-level (or tidal) datums for the Boston tide gauge, as determined by the U.S. National Oceanic and Atmospheric Administration (NOAA) for the epoch 1983–2001, are given in Table 1. Most elevations discussed below are taken relative to the MSL datum. Table 1. Sea Level Datums at Boston, for Epoch January 1983–December 2001a Datum Height (cm) relative to station datum Height (cm) relative to MSL Nuisance flood level 488.5 222.5 MHHW—mean higher high water 420.5 154.5 MHW—mean high water 407.1 141.1 MSL—mean sea level 266.0 0.0 MLW—mean low water 117.8 − 148.2 MLLW—mean lower low water 107.4 − 158.6 NAVD88—North American vertical datum 275.2 9.2 NOAA, National Oceanic and Atmospheric Administration. a All datums were determined by NOAA; see http://tidesandcurrents.noaa.gov. See Sweet et al. [2014] for the “nuisance” flood level. The nuisance flood level quoted in Table 1 is equivalent to the “minor flooding” level for Boston as designated by NOAA's Weather Forecast Office. This flood level is an empirical threshold, based on observations of actual local flooding. Water levels exceeding this threshold, or anticipated to exceed this threshold, are the basis under which a ‘Coastal Flood Advisory’ is issued. The value in Table 1, equivalent to 68 cm above mean higher high water (MHHW), is extracted from Table 1 of Sweet et al. [2014] It is consistent with the nuisance flood level used by Spanger-Siegfried et al. [2014, see Table 1 of their technical appendix]. Annual mean sea levels at Boston, calculated by the Permanent Service for Mean Sea Level (PSMSL) but subsequently adjusted to be consistent with the 1983–2001 MSL datum, are shown in Figure 1. A least-squares linear fit to these data yields a relative sea-level rise rate of 2.79 ± 0.21 mm/y. According to the model of Peltier et al. [2015], 0.50 mm/y of this rise is due to glacial isostatic adjustment following the loss of the great Pleistocene ice sheets. The unusually large positive anomaly in 2010, similarly observed at tide gauges along most of the U.S. east coast where it was associated with increased coastal flooding [Sweet et al., 2009], was apparently caused partly by a weakening of the overturning circulation [Goddard et al., 2015; Ezer, 2015] and partly by anomalous atmospheric pressure loading [Piecuch and Ponte, 2015]. Figure 1Open in figure viewerPowerPoint Annual mean sea levels at Boston, relative to the 1983–2001 mean sea level datum. Individual means were extracted from the archives of the Permanent Service for Mean Sea Level. A linear straight-line fit to the data (dashed line) has a slope of 2.79 ± 0.21 mm/y, where the quoted standard error has been adjusted for autocorrelation. The large positive anomaly in 2010 has been recently discussed by Goddard et al. [2015]. Owing to this 2.79 mm/y sea level rise, Sweet et al. [2014] show that nuisance flooding at Boston has markedly increased in recent years. Before 2010 only one year experienced more than 5 nuisance flooding events. After 2010, three years (of four examined) experienced more than 5 events. Our purpose below is to investigate how often this can now occur from astronomical tides alone. 3 Tidal Prediction for Boston The official Boston tidal predictions routinely published by NOAA are based on NOAA's standard set [Parker, 2007] of 37 tidal constituents. The harmonic constants used for these predictions, available at NOAA's website, are based on measurements obtained over the period 1994–1998 [Jena Kent, pers. commun., 2016]. Owing to the long time period of interest here, the accuracies desired, and some peculiarities of the Gulf of Maine tides, a number of extensions to NOAA's set of constants and how they are employed should be implemented. These extensions are described in the following subsections. Some aspects of the discussion are of a technical nature, and those readers uninterested in details of tidal prediction may skip to Section 4. 3.1 Tidal Constituents The harmonic constants employed below for tidal prediction are based on reanalysis of hourly data collected over the period 1980 January 1 through 2002 December 31, a period somewhat longer than a full lunar nodal cycle (which is 18.6 y). Determining which constituents to include was based on a detailed analysis of the spectrum of tidal residuals, which was computed for the 4-year interval 1997–2000 for which continuous data are available without gaps. Most isolated spectral peaks in the residual spectrum, at least through species 5, could be eliminated with a set of 108 tidal constituents. The highest frequency term kept was M12. Sixth-diurnal terms appear especially pronounced at Boston, and that band had the largest residual energy aside from the semidiurnal band. Some initially estimated constituents were subsequently removed if their standard errors exceeded their amplitudes; failure to do this can result in worse rather than better tidal predictions (as Zetler [1991] emphasized in his final publication). Most of these removed constituents were in the long-period band (period 1 week and longer) where background variability is largest. The largest constituents not in the standard NOAA set are the sixth-diurnal terms 2MN6 and 2MS6, with amplitudes 19 and 13 mm, respectively, and an annual sideline of M2, sometimes denoted MA2, with amplitude 17 mm. Our tide predictions below include the mean seasonal cycle via the annual and semiannual constituents Sa and Ssa. Even though our analysis window differs from that employed by NOAA, our Sa and Ssa constants are reasonably consistent with theirs. Our estimated amplitudes and phase lags are 36 mm and 129° for Sa, 18 mm and 89° for Ssa; NOAA's are 32 mm and 126° for Sa, 18 mm and 90° for Ssa. One of the peculiarities of the Gulf of Maine tides is the relatively large semidiurnal tides arising from the third-degree term in the tidal potential. If we denote these constituents with a superscript 3, the two largest such lines at Boston are 3N2 and 3L2, with amplitudes both about 12 mm. Their frequencies differ from the standard N2 and L2 constituents by 1 cycle in 8.85 y (the lunar perigee period), so estimation of them requires a multi-year time series, as here. Ignoring these lines causes a false 9-y modulation in the standard degree-2 constituents. Cartwright [1975] called attention to a similar case involving a degree-3 diurnal line in the seas off western Europe. 3.2 Secular Changes in Tides Secular changes in tidal harmonic “constants” have been observed at a number of locations [e.g., Cartwright, 1972; Flick et al., 2003; Araújo and Pugh, 2008; Woodworth, 2010]. Changes are especially large in the Gulf of Maine [Ray, 2006], although being near the mouth of the gulf, Boston is experiencing smaller changes than locations to the north. The changes are readily apparent in Figure 2, which shows estimates of the amplitude and phase of the M2 constituent that have been independently computed for each year back to 1922. (The 18.6-year nodal modulation of M2 has been retained in these estimates, for reasons to be discussed shortly.) Over the whole time series shown in Figure 2, the amplitude of M2 has been changing roughly linearly at the rate 2.7 ± 0.5 cm/century. The change in phase lag is − 1.5 ± 0.4∘/century. At Eastport, farther to the north, the M2 amplitude rate is nearly 8 cm/cy, a significant fraction of the MSL rise itself. Figure 2Open in figure viewerPowerPoint Annual estimates of the amplitude (top panel) and Greenwich phase lag (bottom panel) of the principal lunar semidiurnal tide M2. The tides were computed without standard corrections for the 18.6-y nodal modulation since standard corrections are inapplicable here. The solid curves are least-squares fits of a linear straight-line trend plus a 18.6-y sinusoid to each entire time series. The amplitude trend was slightly larger before 1980, then dropped off [Ray, 2006], but has again increased such that year 2014 saw the largest M2 amplitude ever at Boston. The reason for these tidal changes is of considerable geophysical interest, although not especially germane to the topic at hand here. They stem in part from the rise in MSL, which changes the water depth, and hence the tidal resonance properties, of the basin [Greenberg et al., 2012]. But other factors must also be at work, possibly including ocean stratification changes either in the gulf itself or in the surrounding deeper Atlantic [Müller, 2012]. There is interannual variability in these M2 changes. For example, the trend over the 1920–1980 interval is larger, about 4.3 cm/cy [Ray, 2006]. The interannual variations are ignored below, however, in part because a linear trend over the whole time series is a good approximation and in part because only the linear trend can be reasonably extrapolated into the future. The second largest constituent at Boston, N2, also displays an increasing amplitude and a decreasing phase lag, fairly comparable to M2 changes: about 2% per century in amplitude and − 2∘/cy in phase. However, S2, for apparently very different reasons, displays a large amplitude decrease [Ray, 2009]. In the calculations below, only the secular changes in M2 are considered. The changes in S2 are somewhat more nonlinear—hence more unpredictable—than those of M2, and in any event their effect on maximum water levels is partially canceled by the corresponding changes in N2. 3.3 Nodal Modulations Because of their dependence on the moon's declination, all lunar tidal constituents undergo a 18.6-y modulation in both amplitude and phase as the moon's orbit plane precesses—as it tilts nearer, then farther, from the earth's equator. In tidal calculations these modulations are accounted for by standard methods that assume a modulation identical to the modulation in the tidal potential [e.g., Pugh and Woodworth, 2014, Section 4.2.2]. In shallow water it is not uncommon that frictional processes cause these standard methods to fail—or at least become less accurate [Amin, 1985; Ku et al., 1985; Feng et al., 2015]. This is the case at Boston. The 18.6-y nodal modulation of M2 is apparent in Figure 2. A least-squares fit to the annual estimates of Figure 2 yields an amplitude modulation of approximately 2.9%, whereas the standard modulation is 3.7%. The estimated phase modulation of 2.3 is fairly close to the standard 2.1°. A similar analysis of N2 shows its amplitude to be suppressed somewhat more than the M2 amplitude; its modulation is 2.6% versus the standard 3.7%. Its phase modulation is 2.3°, again close to expected. After N2 the next largest lunar tidal constituent at Boston is K1. The observed nodal modulations of K1 are almost consistent with the standard modulations: 11.0 ± 0.3% in amplitude and 8.8° ± 1.3° in phase versus the expected 11.5% and 8.9°. In the calculations to follow, special (i.e., the observed) nodal modulations were used for the M2 and N2 constituents. For all other lunar constituents, which are all significantly smaller than M2 and N2, standard nodal adjustments were deemed acceptable to use. 3.4 Hindcast Test The above details of tidal calculations are sufficiently arcane that the reader may wonder if simply using NOAA's set of 37 constituents with standard tide prediction software is not sufficiently satisfactory. This section therefore summarizes a test of hindcasting tides over the entire Boston time series, comparing the accuracy of a standard approach with one based on modifications as described above—108 constituents, with secular changes in M2 and special nodal modulations for M2 and N2. (Note that this comparison should not be considered a test of a “NOAA prediction,” since the software used here is unique and NOAA's prediction algorithms are surely different in various ways, some possibly subtle, such as how often nodal modulations are updated. More importantly, based on their past operations, NOAA would surely use harmonic constants derived for epochs closer to the periods of the hindcasts.) Figure 3 shows root-mean-square (RMS) errors in predicted hourly elevations, computed for each year of the Boston time series using the two above approaches. The observed tide-gauge elevations have been high-pass filtered with a cutoff around 2 days, which removes most non-tidal variability and leaves mostly tidal signals. Excluding the anomalous year 1971, the two approaches yield a mean RMS error of 7.1 cm versus 5.7 cm, implying a reduction in variance of 18 cm2. The relative improvements with the non-standard algorithm are more marked for the earlier pre-1950 years, presumably owing to the secular trend in M2 and the long interval between the hindcast time and the time period over which NOAA's harmonic constants were determined. The tidal prediction improvement is important for any attempt to predict tides decades into the future. Figure 3Open in figure viewerPowerPoint RMS tide prediction error (cm) computed for each year of the Boston tide-gauge time series. Observed hourly elevations were high-pass filtered to better isolate tidal signals. Blue: Predictions based on National Oceanic and Atmospheric Administration's standard 37 harmonic constituents for Boston, with standard nodal corrections. Red: Predictions based on 108 harmonic constituents, as described in Section 3, accounting for secular trends in the M2 coefficients and using special nodal corrections for M2 and N2. Examination of the anomalous year 1971 (an outlier also in Figure 2) shows erratic gauge data during the first 10 months of the year, suggestive of possible timekeeping errors of roughly 10 min. 4 Predicted High Water This section tabulates all predicted occurrences of tidal high water at Boston that exceeds the nuisance flood level of 68 cm above MHHW. The predictions are based on astronomical tides alone, sitting atop the rising MSL at Boston. The observed MSL curve (Figure 1, but slightly smoothed) is used for times before 2015, but for future events some climate-based scenario is required. Two scenarios are adopted here: Scenario 1 simply assumes that the (approximately) linear twentieth-century rate of 2.79 mm/y will continue indefinitely. Scenario 2 follows the “Intermediate-High” scenario from the U.S. National Climate Assessment [Parris et al., 2012], as adjusted for local conditions following Tebaldi et al. [2012] and publicly released by Climate Central [see also Strauss et al., 2012] That scenario sees MSL at Boston rising 128 mm by 2030 (relative to 2012) and 335 mm by 2050. Scenario 2 has also been used recently by Spanger-Siegfried et al. [2014] in their projections of future flooding for many U.S. cities. Scenario-1 is extremely conservative and must be considered a lower bound. In fact, because existing tide-gauge measurements reveal a recent acceleration in sea-level rise along much of the east coast north of Cape Hatteras [e.g., Boon, 2012], a scenario with increasing future rates seems more realistic than one with a constant rate. Figures 4 and 5 show all predicted high-water events near or exceeding the nuisance-flood level for Scenarios 1 and 2, respectively. The two figures are identical before 2015, since they are based on observed MSL at Boston, not projected MSL. The figures indicate that the first “tide only” nuisance flood occurred in 2011. Even for the conservative Scenario 1, these events will become more and more common in future years. For Scenario 2, the events will become even more common, and the severity (i.e., water level) of floods will gradually increase until by 2040 many will be routinely exceeding 20 cm above flood level. By year 2030 there are 43 flood events for Scenario 1 (i.e., 43 times the predicted high water is found to exceed the nuisance flood level). There are 87 flood events for Scenario 2. By year 2050 there are 213 and 743 events, respectively, for the two scenarios. Figure 4Open in figure viewerPowerPoint Predicted high tides at Boston near or exceeding the “nuisance flood” level of 68 cm above mean higher high water. Before 2010, the tides alone never exceeded flood levels; any flood experienced in Boston required assistance from meterological conditions such as severe storms. In 2011 and afterwards, sea level has risen sufficiently that tides alone can produce nuisance flooding. For years after 2015, the scenario for projected mean sea level (MSL) rise adopted for this figure is a simple linear extrapolation of the historical Boston MSL trend. Compare with Figure 5. Figure 5Open in figure viewerPowerPoint As Figure 4, but for mean sea level following “Scenario 2” for years after 2015. Scenario 2 is the “Intermediate-High” scenario of the latest U.S. National Climate Assessment, adjusted for conditions at Boston [Tebaldi et al., 2012] and made available by Climate Central. More detailed information for the first nusiance floods of Scenario 1 is given in Table 2. Complete tabulations through 2050 are available as supplementary files to this paper. The first few entries, up until time of this Table 2. First “Tide Only” Flooding Occurrences at Bostona Date Predicted High Water Observed High Water UTC H (cm) UTC H (cm) April 19, 2011 04:13 222.7 04:06 221.4 October 27, 2011 15:44 224.6 15:52 228.9 October 28, 2011 16:35 224.9 16:30 226.8 May 07, 2012 04:08 227.9 04:13 216.6 May 08, 2012 05:01 227.1 05:06 217.7 June 05, 2012 03:53 226.5 03:54 255.4 June 06, 2012 04:47 223.8 04:48 238.3 November 14, 2012 15:41 222.5 15:42 223.6 November 15, 2012 16:32 225.0 16:22 228.1 December 13, 2012 15:22 223.1 15:34 211.5 December 14, 2012 16:15 224.6 16:06 210.7 May 26, 2013 04:09 222.3 04:17 232.3 May 27, 2013 05:01 224.0 05:03 214.5 June 24, 2013 03:53 225.7 03:59 222.7 June 25, 2013 04:47 225.9 04:39 226.7 May 08, 2016 04:32 224.4 04:38 238.6 November 15, 2016 16:03 224.3 November 16, 2016 16:55 222.6 May 27, 2017 04:29 227.2 May 28, 2017 05:23 224.6 MSL, mean sea level. a All elevations H are relative to the 1983–2001 MSL datum. writing (2016), may be compared with actual measurements from the Boston tide gauge. For that purpose the corresponding observed high waters were extracted from NOAA's 6-min elevation time series, with the peak times and elevations estimated by interpolation with a modified cubic spline. There is some scatter about the predicted values—an expected effect arising from the non-tidal forcing of sea level—but the mean of the 16 observed-minus-predicted elevation differences is only 0.8 cm; the standard deviation is 11.4 cm; the maximum difference is 29 cm, obtained on 5 June 2012 when sea level reached 255 cm above MSL. There were, of course, other non-tidal flooding events during this period. In fact, one event, obviously related to the June 5 weather, occurred only one day before, at 2:48 on June 4, when sea level reached a comparable 253 cm while the predicted tidal contribution peaked at 211 cm, 11 cm below flood level. (Times quoted here are UTC.) Since the predicted floods of Figures 4 and 5 are completely of tidal origin, the duration of any one flood must be relatively short. After all, low tide will always occur roughly six hours later. Especially for those cases when predicted high water barely breaches flood level, the duration of flood may be only a few minutes; the very highest tide, reaching 256 cm on 29 May 2048 for Scenario 2, lasts 2.3 h. One common way to characterize predicted flooding is in terms of number of hours (per year, say) when water levels are expected to exceed flood level. Using our predicted water level curves, we have computed such annually integrated flood-duration times. The results, shown in Figure 6, complement the high-water diagrams of Figures 4 and 5, and they again serve to emphasize the contrast between our two adopted MSL scenarios. While the two scenarios display only minor differences in flood duration times through the early 2020s, beginning around 2030 the differences are stark. For Scenario 1 there are occasional years, even through 2041, when predicted water levels are above flood level for only a few minutes per year. This is also evident from Figure 4. For Scenario 2 integrated duration times eventually exceed 80 h per year. This large number is a reflection of the great number of floods per year and also the generally greater elevations, hence longer durations, of many of those floods, as is clear from Figure 5. Figure 6Open in figure viewerPowerPoint The number of hours per year that predicted water levels exceed nuisance flood levels, for the two different mean sea level scenarios. Note that any one flood, since solely tide-driven, is of fairly short duration. Thus, duration totals exceeding tens of hours per year reflect a large number of individual nuisance floods, as is also clear from Figures 4 5. 4.1 Pattern of the Tidal Flooding at Boston There are some clear temporal patterns in the predicted high water as shown in Figures 4–6 and Table 2. Certain years, and certain times within a year, tend to be more prone to flooding. These patterns are a function of the tidal regime, or the relative amplitudes of certain major constituents [e.g., Zetler and Flick, 1985]. A location with purely semidiurnal tides would experience all these highest-water times during the equinox seasons [Cartwright, 1974; Amin, 1979]. Semidiurnal tides are maximized when the declination of both sun and moon are minimal, and this occurs around times of equinox. In term of tidal constituents, it is the semidiurnal “declinational” constituent, K2, that models this effect and forces highest spring tides toward the equinox. A glance at Table 2, however, suggests a tendency for high water to occur more often at times closer to solstice. In fact, while one might think of Boston tides as primarily semidiurnal, the diurnal K1 and O1 constituents are large enough (15 and 11 cm, respectively) and K2 small enough (6 cm) that the highest waters tend to occur when the diurnal contributions are most pronounced, which occurs at maximum, not minimum, declinations, i.e., at winter or summer solstice. The seasonal cycle in sea level, in the form of constituents Sa and Ssa which when summed together peak in early June, also contributes as well. The result is robust: tabulating the time of year of all flood events of Figure 4 leads to the histogram of Figure 7, showing the preponderance of flooding around late spring and early summer and also late autumn and early winter. Figure 7Open in figure viewerPowerPoint Histogram showing time of year of all flood events from Figure 4. Vertical dashed lines mark times of spring and fall equinox and summer and winter solstice. Tide-only floods tend to occur near summer s
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