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Tidal amplitude decreases in response to estuarine shrinkage: Tokyo Bay during the Holocene
Estuarine, Coastal and Shelf Science 225 (2019) 106225
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Tidal amplitude decreases in response to estuarine shrinkage: Tokyo Bay during the Holocene
T
Katsuto Ueharaa,∗, Yoshiki Saitob,c a
Research Institute for Applied Mechanics, Kyushu University, 6-1 Kasuga Koen, Kasuga, Fukuoka, 816-8580, Japan Estuary Research Center, Shimane University, 1060 Nishikawatsu-cho, Matsue, Shimane, 690-8504, Japan c Geological Survey of Japan, AIST, 1-1-1 Higashi, Tsukuba, Ibaraki, 305-8567, Japan b
A R T I C LE I N FO
A B S T R A C T
Keywords: Estuaries Tides Sea level changes Palaeoclimate Tidal resonance
Tidal changes in Tokyo Bay during the last 10,000 years were investigated by combining a numerical model with newly compiled model bathymetries for the present day, the early 20th century, and every 1000 years from 4000 to 10,000 years ago. Over this time period, sea level has changed by more than 30 m, and the coastline has shifted 50–60 km. Tides during the early 20th century and 4000–9000 years ago were larger than those at present; from 9000 to 4000 years ago, the bay setting was mesotidal, in contrast to the modern microtidal setting. The maximum tidal level at the head of the bay was 72% higher 7000 years ago than at present, and M2 tidal currents at the bay mouth from 10,000 to 9000 years ago were three times stronger than those at present. When tides were compared at a fixed location, the greatest tidal enhancement was found to have occurred 9000 years ago. The weakening of tides over the last 9000 years can be explained by introducing the concept of estuarine shrinkage together with quarter-wavelength resonance theory. Tidal weakening occurred in two phases: during the first phase, 9000–7000 years ago, it was due to the rise in sea level (type 2 shrinkage), and during the second phase, a decrease in the length of the bay was responsible (type 1 shrinkage). These findings can be applied to the assessment of both past tidal changes and potential future tidal changes in other elongated estuaries with lengths of several tens of kilometers.
1. Introduction Many estuaries and embayments in East and Southeast Asia have experienced extensive coastline changes since about 20,000 years ago (20 ka), the time of the last glacial maximum (LGM). From the LGM to the mid-Holocene (where the Holocene encompasses the last 11.7 × 103 years or 11.7 kyr; Walker et al., 2018), a sea-level rise of more than 100 m along receding coastlines led to the formation of drowned valleys. Subsequently, during the middle to late Holocene, when sea level remained stable or fell by several meters, these valleys became filled with sediment and the coastline shifted seaward (Umitsu, 1991; Hori and Saito, 2007; Endo, 2015). Among embayments in Japan, Tokyo Bay (Fig. 1) is one of those where the millennium-scale coastline changes were first investigated (e.g. Toki, 1926). It is estimated that during the period of maximum transgression in the mid-Holocene, the landward retreat of the coastline by more than 60 km relative to its current position led to the formation of an inner bay called Oku (or Upper) Tokyo Bay (Kaizuka et al., 1977). Tidal characteristics in estuaries and embayments depend primarily
∗
on the embayment shape, and they are therefore susceptible to changes in coastlines and sea level (Pickering et al., 2017; de Haas et al., 2018; Schindelegger et al., 2018). Thus, tides in Tokyo Bay are expected to have experienced large modifications during the Holocene. Fujimoto (1990) developed a linear analytical model for Tokyo Bay in the midHolocene and inferred that the tidal range exceeded 7 m at maximum transgression, more than four times the present tidal range. Although this mid-Holocene tidal enhancement is plausible (indeed, it is confirmed in the current study), the model seems to have overestimated the tidal range, probably because, in this pioneering work, Fujimoto (1990) assumed frictionless and uniform-depth settings and also because the obtained result was beyond the applicable range of the linear theory. Since the 1980s, a number of tidal simulations have been carried out to reconstruct Holocene tides in various oceans and coastal seas around the world (for reviews see Hinton, 1997; Griffiths and Hill, 2015; Ward et al., 2016). These studies suggest that, during the early Holocene, semi-diurnal tides were enhanced especially in the North Atlantic Ocean (e.g., Thomas and Sündermann, 1999; Egbert et al., 2004; Uehara et al., 2006; Arbic et al., 2008; Green et al., 2009; Hill et al.,
Corresponding author. E-mail address: [email protected] (K. Uehara).
https://doi.org/10.1016/j.ecss.2019.05.007 Received 7 September 2018; Received in revised form 26 April 2019; Accepted 18 May 2019 Available online 20 May 2019 0272-7714/ © 2019 Elsevier Ltd. All rights reserved.
Estuarine, Coastal and Shelf Science 225 (2019) 106225
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Fig. 1. (a) Map of the study area. Red lines denote the location of sections shown in Fig. 5; the solid line follows the paths of the Ko (Paleo) Tokyo River and the paleo–Naka River whereas the broken line is aligned with the axis of the modern bay. Black dotted lines indicate the maximum extent of the Holocene transgression (cf. Kosugi, 1989) and blue solid lines indicate the position of major river channels. Symbols in diamond indicate the location of tide-gauges—MK: Makuchi, YS: Yokosuka, YH: Yokohama (Shinko), HM: Harumi, CL: Chiba Light. Other abbreviated features represent AL: Arakawa Lowland, NL: Nakagawa Lowland, TL: Tokyo Lowland, KS: Kawasaki, NS: Nakanose Shoal, FS: Futtsu Spit, CK: Cape Kannon. Two black broken lines denote the location of the northern and southern limit of the Uraga Strait. (b) Map of the model domain. Color shadings show geological structures according to land-usage maps issued by Geographic Institute of Japan. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)
rectangle about 60 km long and 20 km wide (Fig. 1a). Though the bay's average depth is about 18 m, a submarine channel with a water depth greater than 40 m is developed along the western side of the bay south of 35.4°N. The channel deepens to about 70 m at the bay mouth and becomes as deep as 700 m at the southern end of the Uraga Strait, at about 35.05°N. To the east of this channel, an isolated mound called the Nakanose Shoal is separated from coastal shoals by narrow channels on its eastern and western sides (Fig. 1a). The shoal, which consists of consolidated sediments of mid-Pleistocene age, is at a water depth of 13–17 m (Hosoya et al., 2002). A remnant of the channel developed during the last glacial sea-level lowstand, when most of the modern bay area was exposed subaerially, can be traced northward along the western side of the modern bay. This largely buried channel is called the Ko (or Paleo) Tokyo River (Chujo, 1962). During the lowstand, fluvial processes eroded Pleistocene terraces that had formed during the last interglacial (ca. 120 ka), and rivers flowed in incised valleys into the Ko Tokyo River. From the latest Pleistocene to the mid-Holocene, sea level rose rapidly, and seawater filled these valleys (Kaizuka et al., 1977). This transgression, called Jomon Kaishin, was most extensive on the northwestern side of the modern bay, where submergence of the paleo–Arakawa (Ara River) and paleo–Nakagawa (Naka River) valleys formed an inner bay called Oku Tokyo Bay (Fig. 1b). Sea level at the time of maximum transgression has been estimated to have been several meters higher than the present sea level (Umitsu, 1991), and Oku Tokyo Bay may have been as long as 50–60 km (Esaka, 1972; Kosugi, 1989). Since the mid-Holocene, sea level has remained stable or has fallen by several meters, and progradation of the river deltas has shifted the coastline to its present position. The modern lowlands (Fig. 1b) formed by the filling of the incised valleys with sediments; the Nakagawa, Arakawa, and Tokyo lowlands, have elevations of less than 5–7 m above mean sea level (Tanabe et al., 2015). The fine, soft sediments that filled the incised valleys during the latest Pleistocene and Holocene are known as the Chusekiso layer. They have a maximum thickness of more than 70 m in the relict valley of the Ko Tokyo River (Endo, 2015). In the northern part of the modern Tokyo Bay, the Chusekiso layer has been divided into two sublayers. The lower fluvial deposits (Nanagochi Formation) were deposited during the latest Pleistocene, and the upper marine deposits (Yurakucho Formation)
2011) and diurnal tides in the South China Sea (Uehara, 2005; Griffiths and Peltier, 2009). Arbic et al. (2008) and Hill (2016) describe the basic concepts of such simulations. To date, however, the only numerical attempt to reconstruct paleotides in Japanese coastal waters is that by Tojo et al. (1999), who used a one-dimensional numerical model to correlate the growth pattern of fossil bivalve shells with paleotides in Osaka Bay. The estimation of paleotides in Japanese embayments is hindered primarily by the presence of thick Holocene deposits filling the relict valleys; these deposits make it difficult to reconstruct paleodepths during specific time periods. In the last decade, however, sequencestratigraphy models applied to the lowlands north of modern Tokyo Bay, a major depocenter, have provided detailed three-dimensional paleodepth information (e.g. Tanabe et al., 2015). The objectives of this study were twofold. First, to provide basic information on paleotides in Tokyo Bay during the last 10 kyr, when seawater filled the main portion of the bay. Second, to examine the basic mechanisms of tidal changes in estuaries and embayments having a spatial scale of tens of kilometers to assess how modifications of sea level and coastlines can alter tidal features. This study is a first attempt to use a two-dimensional model to estimate changes in paleotides in Japanese embayments. To accomplish these objectives, we prepared high-resolution paleobathymetries incorporating the latest information on Holocene sediments in the Tokyo Bay area, one of the most densely investigated regions of Japan. 2. Regional setting Tokyo Bay, central Japan, is bounded by the Kanto Plain on the north, the Miura Peninsula on the southwest, and the Boso Peninsula on the southeast; on the south, it is connected to the Pacific Ocean via the Uraga Strait (Fig. 1). The offshore boundary of the modern bay is commonly considered to be the northern end of the Uraga Strait, along a line connecting Cape Kannon and Futtsu Spit, where oceanic ecological and hydrographic features switch to inner-bay conditions. In this study, however, we defined the bay area as the entire embayment north of 35.25°N, the latitude of Cape Kannon, because Futtsu Spit did not exist during the early to middle Holocene. The modern bay can be approximated by a northeastward-tilted 2
Estuarine, Coastal and Shelf Science 225 (2019) 106225
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Because the present-day bathymetry includes artificial features such as reclaimed land and dredged channels, we reconstructed the bathymetry during the 1920s–1930s (referred to hereafter as the “early 20th century” or “1930″ bathymetry) by referring to navigational charts issued from 1924 to 1936 (Fig. 2b). Although the area of the bay during that period was 28% larger than at present, its average depth was lower by 18% because of the presence of shoals developed along the northern coast. We used this bathymetry as a reference in our compilations of paleobathymetry data.
were deposited mainly during the Holocene (Tanabe et al., 2010). The Yurakucho Formation is often further subdivided into lower and upper units, which are considered to have been deposited during the retreat and advance of the shoreline, respectively (Ishiwata, 2004). Most of the coastline north of 35.33°N has been modified by human activities such as land reclamations and seawall constructions, mainly during the 1960s and 1970s (Endo, 2004). In the northeastern and eastern parts of the bay, a pre-Holocene basal platform extends seaward from the coast; this platform, which formed by wave action, is buried at water depths of 10–20 m (Kaizuka et al., 1977).
3.2. Paleobathymetries
3. Methods
Paleobathymetries from 10 ka to 4 ka (Fig. 2c–i) were reconstructed by referring to multiple sources, as outlined below. The dataset was newly compiled because no comprehensive dataset covering Tokyo Bay as a whole existed. The compiled dataset incorporates outcomes of sequence-stratigraphy models that include detailed isochrones for the Holocene layers for three regions: the Nakagawa and Tokyo lowlands south of 36°N (Kimura et al., 2006; Tanabe et al., 2015), the Arakawa Lowland (Komatsubara et al., 2017), and the Obitsu River delta (Saito, 1995). We referred to geological cross sections to reconstruct bathymetries of the northwest coast of the modern bay (Bureau of Port and Harbor, 2001; Ishiwata, 2004; Ishihara et al., 2013), the Tama River delta (Matsuda, 1973; Matsushima, 1988), the Yokohama area (Matsushima, 2010), the Yokosuka area (Matsushima et al., 2016), and the Futtsu Spit (Saito and Kayanne, 1991), and we also used two sections transecting the bay at about 35.3°–35.5°N (Akutsu, 1973; Shirai et al., 2004). Where date information was not available in the geological records, the boundary between the Nanagochi and Yurakucho formations was
Paleotides were reconstructed using a two-dimensional tidal model based on paleobathymetry data for specified times, namely, two times in the modern era when Oku Tokyo Bay was not extant (the present day and early 20th century), and every 1 kyr from 4 ka to 10 ka, when a marine environment prevailed in Oku Tokyo Bay, north of the modern bay. All dates in this study are presented as calibrated years. 3.1. Modern bathymetries Bathymetric data used for tidal reconstruction were defined on a longitude–latitude grid covering longitudes from 139.51°E to 140.17°E and latitudes from 35.15°N to 36.24°N with a resolution of 0.01° (ca. 1 km). For the present-day bathymetry of Tokyo Bay (Fig. 2a), we compiled data from electronic navigational charts issued in 2014 (in Figs. 2–6, results based on this bathymetry are labeled as “2014″). Water depths obtained from the charts were raised by 1 m to correct for the difference between mean sea level and the chart datum.
Fig. 2. Model bathymetries used in this study. Light and dark gray shadings indicate areas having elevation of 10–15 m and over 15 m relative to the modern sea level, respectively. The depths are measured downward from the mean sea level at each time slice. 3
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Fig. 3. Horizontal distribution of the maximum elevation predicted by the numerical model. The contour interval is 0.05 m.
∂η/∂t + ∇·U = 0,
correlated with the base of the Holocene, and the boundary between the upper and lower units of the Yurakucho Formation was considered to approximately coincide with the maximum transgression. In areas where detailed geological information was not available, we used the depth of the base of the Chusekiso layer to constrain the lower limit of Holocene sediments. For this purpose, we referred to several maps (e.g. Kaizuka et al., 1977; Endo et al., 2013) and to Submarine Geological Structural Charts issued by the Japan Coast Guard showing the depth of the layer's base. Where the present-day sea is deeper than 10–20 m, the reconstructed paleodepths include large uncertainties because, aside from the two submarine sections mentioned above, the depth of the Chusekiso layer base was the only information available. In this study, following Tanabe et al. (2015), we assumed that the maximum transgression occurred at 7 ka, except in the paleo–Arakawa Valley, where the coastline started to advance seaward at 8 ka (Komatsubara et al., 2017). We adopted the sea-level curve of Tanabe et al. (2015), as modified from that of Endo et al. (1989), to determine paleodepths. Relative to the present, sea level was assumed to be −30 m at 10 ka, −17 m at 9 ka, −5 m at 8 ka, +3 m during 7–6 ka, +1 m at 5 ka, and the same as present during the last 4 kyr.
where U = Du, u the horizontal current vector, D = H + η the thickness of the vertical column, H the undisturbed depth, η the surface elevation relative to mean sea level, f the Coriolis parameter, k the unit vertical vector, × the vector cross product, g the gravitational acceleration (=9.806 m/s2), ∇ the horizontal gradient operator, cD the bottom drag coefficient (= 0.0025), and Ah the horizontal viscosity coefficient (= 100 m2/s). We adopted the numerical scheme of Pelling et al. (2013) to handle tides in intertidal zones. Each experiment was conducted on a 0.01° × 0.01° grid for 45 days from rest, and the last 29.53 days (a synodic month) were used for the analysis. The same model settings, except for the bathymetry, were used for all experiments. In the model, tides are driven by specifying the surface elevation along the offshore open boundary. This boundary value was compiled from the harmonic constants of four major tidal components recorded at the Makuti tide-gauge station (amplitudes 37.3 cm, 16.8 cm, 22.9 cm, and 19.7 cm for M2, S2, K1, and O1 tides, respectively; Japan Coast Guard, 1992). The discrepancy between the observed and simulated present-day tides at the four tide-gauge stations, Chiba-light, Tokyo (Harumi), Yokohama (Shinko), and Yokosuka, was 1.6 cm (root-meansquare difference) or 3.5% (mean relative deviation) in the case of the M2 amplitude and 1.8° (root-mean-square difference) in the case of the M2 phase. Because this discrepancy in tidal amplitude is close to the resolution of the sea-level measurements (1 cm) and smaller than the difference in the maximum tidal amplitude between the present-day and early 20th century cases (ca. 4 cm; section 4), we consider the accuracy of the model to be sufficient to resolve tidal changes in the study area. In this study, the tides at the offshore open boundary were assumed
3.3. Tidal model We introduced a two-dimensional tidal model based on Uehara et al. (2006) and Pelling et al. (2013) to estimate present-day and past tides and tidal currents. The model formulations and range of parameters adopted are comparable to those commonly used for tidal models of present-day coastal seas: ∂U/∂t + (u·∇)U - f k × U = - gD∇ η - cD|u|u + Ah∇·(D∇u),
(2)
(1) 4
Estuarine, Coastal and Shelf Science 225 (2019) 106225
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Fig. 4. Horizontal distribution of M2 velocity amplitudes predicted by the numerical model.
Fig. 5. (a) Changes in the maximum elevation along a section aligned with the axis of the modern bay (cases 2014 and 1930; red dashed line in Fig. 1a) or with that of the paleo-bay (other cases; red solid line in Fig. 1a). (b) Same as Fig. 5a except for M2 and K1 amplitudes and that values in intertidal zones are not shown. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)
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4.1.2. Harmonic constants At each time slice, the horizontal pattern of the amplitudes of the four major tidal constituents was similar to that of the maximum elevations shown in Fig. 3, except that the amplitudes were small in intertidal areas (not shown). The tidal amplitudes increased toward the bay head and across-axis variations were small. Tidal phases lagged toward the bay head; for diurnal tides, the lag in the interior region north of about 35.4°N was about 5°, and for semi-diurnal tides it was 10°. In addition, phases were advanced by 1°–2° on the eastern side compared to the western side of the bay. This east-west tidal-phase asymmetry was not apparent in test runs conducted without taking account of the Coriolis force, so the asymmetry is likely due to the Coriolis effect. 4.1.3. M2 tidal velocity Fig. 4 illustrates the horizontal distribution of M2 tidal current amplitudes, the strongest tidal component in the study area. Most of the simulated tidal current ellipses were rectilinear (unidirectional) and aligned parallel to the bay axis, so only the amplitudes are shown in the figure. At all time slices, the strongest M2 tidal current was observed around the bay mouth; the speed was 0.33 m/s in the present-day case, 0.45 m/s during the early 20th century, 0.7–0.8 m/s during 4–7 ka, and 0.9–1.0 m/s at 8 ka and earlier. These results indicate that the maximum M2 current was about three times stronger during the early Holocene than it is at present and that the maximum current speed has decreased over time. During 6–8 ka, the bay mouth was wider than at present because Futtsu Spit did not yet exist. Additional test runs with paleobathymetries modified to include Futtsu Spit showed that when the bay mouth was wider (i.e., simulations without the spit), the tidal current around the bay mouth was weaker than in simulations with the spit. Strong tidal currents were distributed mainly in three areas: the bay mouth region south of about 35.4°N, a constricted area north of the modern bay, and the northern part of the paleo–Nakagawa Valley. The locations of intense tidal currents at each time slice did not differ greatly between diurnal and semi-diurnal tides; this result suggests that the position of energetic currents was controlled mainly by local topographic conditions rather than by basin-wide tidal dynamics. East of 139.95° E, M2 tidal currents were weaker than 0.1 m/s from 8 ka. This result indicates that the influence of tidal currents in northeastern and eastern part of the modern bay has been small since 8 ka, and is consistent with previous findings based on geomorphological analyses that erosional features such as the submarine terraces found in this area were formed by wave actions (Kaizuka et al., 1977). At all time slices, the phase difference between the tidal elevation and the tidal current was 80°–90° in most regions (not shown); this result suggests that the tidal waves in the bay behaved as standing waves, not as progressive waves.
Fig. 6. Tidal response curves at different time slices as a function of the tidal forcing period. Two vertical gray lines denote the period of M2 and K1 tides.
to be the same as at present in all cases for two reasons. First, global paleo-ocean tide simulations indicate that tidal changes in the northwest Pacific Ocean have been small during the last 20 kyr (e.g. Egbert et al., 2004; Uehara et al., 2006; Griffiths and Peltier, 2009). Second, relative sea levels reconstructed by the latest glacial isostatic models show large discrepancies around the study area (e.g. about −10 m at 10 ka; Peltier, 2004; Peltier et al., 2015) with those reconstructed by using local proxy records (e.g. −30 to −40 m at 10 ka; Endo, 2015; Tanabe et al., 2015). Because at present the performance of global paleo-ocean tide models depends greatly on the output of isostatic models, it was not possible to retrieve open-boundary values from global paleotidal models that were consistent with the paleobathymetries determined by using local geological records.
4. Results 4.1. Horizontal distributions 4.1.1. Maximum tidal elevations Numerical simulation shows the horizontal distribution of maximum tidal elevations, i.e. the highest tidal elevation in a synodic month (29.53 days); this includes the contribution of compound tides, which was large in intertidal zones (Fig. 3). In the case of present-day Tokyo Bay, the simulated maximum elevation is comparable to the mean high water spring (MHWS) or half the spring tidal range. For example, MHWS computed from the tide-gauge record at the Chibalight station from 1995 to 2013, 0.74 m, is comparable to the modelsimulated maximum elevation of 0.77 m. At all time slices, the maximum elevation increased toward the bay head along a line parallel to the bay axis, whereas the across-axis variation was small. In the area occupied by the present-day bay, the maximum elevations during 4–9 ka were higher than those at present. Tidal elevations during the early 20th century were also higher than those at present, consistent with the numerical study results for M2 tides reported by Yanagi and Ohnishi (1999). Although the maximum elevation was highest in the northeastern corner of the bay during the modern eras (Fig. 3a and b), the highest values at 4 ka and before were observed at the head of the paleo–Nakagawa Valley. An exception was at 8 ka (Fig. 3g) when the paleo–Arakawa Valley was most extensive. The maximum elevation was slightly higher at the head of the paleo–Arakawa Valley than at the head of the paleo–Nakagawa Valley. During 9–7 ka, maximum elevations at the paleo–bay head exceeded 1.25 m, and during 6–4 ka, they exceeded 1.1 m.
4.2. Along-axis profiles To examine the tidal changes in more detail, we constructed profiles of the maximum levels and amplitudes of the M2 and K1 tidal constituents along sections parallel to the bay axis (Fig. 5). The section for 4–10 ka follows the paths of the Ko Tokyo River and the paleo–Naka River, and the section for the two modern periods is aligned with the axis of the modern bay north of 35.5°N (see Fig. 1a). The amplitudes of the S2 and O1 tidal constituents are not shown, but their profiles were similar to those of the M2 and K1 constituents, respectively. The maximum elevation increased monotonically toward the bay head, except at 10 ka, when the elevation decreased slightly near the bay mouth (Fig. 5a). The highest maximum elevation of 1.34 m, which was observed at 7 ka, is about 72% larger than that at present. The maximum elevation was higher than 1 m along the section north of 35.7°N during 4–9 ka and around the bay head at 10 ka. Because the 6
Estuarine, Coastal and Shelf Science 225 (2019) 106225
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the M2 constituent and 12 h for the S2 constituent), and the resonance period basically became shorter over time. During 9–10 ka, the tidal response peaks were smaller and broader compared with those for the other time slices. These peak characteristics are attributable to a higher level of dissipation caused by the narrow configuration of the bay and shallow water depths during these time slices. The major features of the observed tidal changes can be explained by the changes in the resonance period. The most enhanced semidiurnal tides emerged during the early Holocene, when the resonance period was closest to the semi-diurnal period. Over time the resonance became shorter, and the difference between the resonance period and the semi-diurnal period increased. The greatest enhancement of the semi-diurnal tides was observed at 9 ka, probably because the bay at 10 ka was shallow (the average depth about 9 m) and narrow and the influence of friction was large, as was suggested by a broad and less distinctive peak feature of the response curve for 10 ka (Fig. 6). The invariable nature of the diurnal tides in terms of both time and space can be attributed to the fact that the forcing period differed greatly from the resonance period. As a result, the tidal response was less sensitive to shifts in the resonance period.
maximum elevation is comparable to MHWS or half the mean spring tidal range (see section 4.1.1), the spring-tide condition in the upper bay during 4–10 ka must have been mesotidal (tidal range 2–4 m), different from the microtidal (tidal range less than 2 m) condition at present. When tides were compared at a fixed location, the maximum elevation was found to be highest at 9 ka along the main part of the section north of the channel adjacent to the Nakanose Shoal at about 35.45°N. Similar to their maximum elevations, amplitudes of the M2 and K1 tidal constituents increased toward the head of the bay (Fig. 5b), except in intertidal zones, where amplitudes of major tidal constituents were small because the lower limit of low tide levels was suppressed by the presence of tidal flats (not shown). Tidal amplitudes within the bay behaved quite differently between semi-diurnal (M2 constituent in Fig. 5b) and diurnal (K1 constituent) tides in terms of both space and time. At all time slices, changes in tidal amplitudes toward the bay head were more evident for M2 tides than for K1 tides. In addition, the ratio of the M2 amplitude at the bay head to that at the bay mouth (both measured along the section) decreased greatly over time, from 2.1 at 9 ka to 1.2 at present, in contrast to that of the K1 amplitude, which remained around 1.1 at all time slices. This result indicates that the past enhancement of tides was due mainly to the greater development of the semi-diurnal tides. For example, 93% of the difference in the highest maximum elevation between 9 ka (at 36°N, south of the intertidal zone) and the present can be explained by the amplitude change of the M2 and S2 tides between those two time slices. As a result, the contribution of semi-diurnal tides to maximum elevations in the upper bay was higher prior to 4 ka than at present. In the present-day case, the ratio of diurnal (K1 and O1) to semi-diurnal (M2 and S2) tides decreased from 0.79 at the offshore model boundary to 0.63 at the head of the bay. At 9 ka, the ratio at the bay head further decreased to 0.42. Thus, semi-diurnal tides were more dominant during the early to middle Holocene than at present. In contrast to the pattern in maximum elevation (Fig. 5a), the largest M2 amplitude was lower at 7 ka than during 9–8 ka, even though the area of the bay was largest at 7 ka (Fig. 5b). When tides were observed at a fixed location, the M2 amplitude, like its maximum elevation, was largest at 9 ka in the interior region north of about 35.45°N but decreases in the M2 amplitude did not occur uniformly through time (Fig. 5b). For example, the smallest M2 amplitudes during 9–4 ka were observed at 6 ka along the section north of 35.4°N.
5.2. Impact of bay length and water depth The basic process leading to shifts of the resonance period can be explained by simple quarter-wavelength resonance theory, which relates the resonance period Tp of a one-dimensional, constant-depth frictionless channel to the channel length l and the mean water depth H
Tp = 4l/ gH
(3)
Although this theory does not take account of effects such as friction, radiation damping (Miles and Munk, 1961), and changes in the depth and width of a bay (Friedrichs, 2010), the simulated paleotides in Tokyo Bay fulfill the background assumption that the tide behaves as a standing wave, and its amplitude increases monotonically toward the bay head. In the case of Tokyo Bay, where the resonance period was found to be shorter than semi-diurnal tidal periods, diurnal and semi-diurnal tides are expected to become weaker as the resonance period Tp becomes shorter. According to Eq. (3), if the water depth increases or the length of the bay decreases, the resonance period will become shorter. We confirmed this relationship by conducting additional experiments for 7 ka in which the water depth was decreased by 1 m or the northern end of the bay was truncated. Tidal changes associated with the shift of resonance period were caused by the combined effects of variation in depth and length. Our results indicate that the simulated decrease in M2 amplitudes from 9 to 7 ka was caused primarily by the effect of the depth increase associated with a large sea-level rise, which seems to have overcome the effect of tidal strengthening due to the increase in the bay length. Further weakening of M2 tides from 7 to 6 ka, during the initial phase of delta progradation at the bay head (Fig. 7a), was caused mainly by the truncation of the bay length. The slight increase in tidal amplitudes during 6–5 ka and 5–4 ka, when the sea level was inferred to have dropped by 2 m and 1 m, respectively, was due mainly to the shoaling of the bay caused by the sea-level change and also by infilling of the incised valleys in Oku Tokyo Bay (Fig. 7b and c). The infilling might have contributed more to the shoaling of the bay than the sea level change, because the tidal enhancement was more apparent within Oku Tokyo Bay north of 35.7°N (Fig. 5b). Finally, the large decrease in tidal amplitudes during the last 4 kyr can be explained by the truncation of the bay length caused by river delta progradation. While the enhanced tides simulated during 9–4 ka seem to represent a robust feature, the detailed pattern of the estimated tidal changes, such as the slightly enhanced tidal amplitudes during 5 ka and 4 ka, might be modified in the future by more refined paleotopographic
5. Discussion 5.1. Shift of the resonance period As shown in section 4.2, temporal changes in the M2 amplitude were not directly linked to changes in the area occupied by the bay. The amplitudes were largest at 9 ka, decreased over time until 6 ka, and then increased slightly during 5–4 ka (Fig. 5b), even though the bay area was largest at 7 ka. Here, we examine the sensitivities of tidal amplitudes to sea level and water depth in relation to shifts in the resonance period of the bay. First, we estimated tidal response curves as a function of the tidal forcing period so that we could numerically infer the resonance period of the bay at different time slices (Fig. 6). The curves were drawn by conducting a series of numerical runs in which tides forced by water levels at the open boundary oscillated with an amplitude of 37.3 cm in a single period ranging between 2.4 and 26 h. The largest tidal amplitude observed in each run was then plotted. The tidal period resulting in the maximum tidal response was about 6.0 h for the present-day setting, which is consistent with the observed resonance period of the bay at present (Unoki, 1993), and it was 6.8 h for the early 20th century case, around 8 h during 4–7 ka, 8.6 h at 8 ka, 10 h at 9 ka, and 12 h at 10 ka. Thus, the resonance period of Tokyo Bay during the last 10 kyr was comparable or shorter than the semi-diurnal tidal period (12.42 h for 7
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Fig. 7. Depth changes taken place in (a) 7–6 ka, (b) 6–5 ka, and (c) 5–4 ka, when the bay become smaller in area and shallower in depth. The difference presented in color shadings are drawn only on the sea area at the newer age. Thick lines denote the coastline at the older age. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)
decrease of tides since the early Holocene by introducing the concept of estuarine shrinkage. From the middle to late Holocene, delta progradation truncated the bay, and the shorter bay length worked to weaken the tides. We refer to a reduction of bay length leading to tidal weakening as type 1 estuarine shrinkage (Fig. 8a). The weakening of tides from the early to middle Holocene, caused by the increase in water depth associated with the sea-level rise, can also be regarded as due to shrinkage of the embayment relative to the length of the tidal waves, because tidal wavelength is proportional to the square of water depth and thus increases when the water depth increases. Therefore, we call shrinkage due to a sealevel rise accompanied by tidal weakening as type 2 estuarine shrinkage (Fig. 8b). To summarize, the overall decrease in tidal amplitudes during the last 9 kyr occurred in two phases by different mechanisms: during the first phase, type 2 estuarine shrinkage was caused by the large sea-level rise during the early to middle Holocene, and it was succeeded during the second phase by type 1 estuarine shrinkage caused by river delta progradation (Fig. 8e). These mechanisms are applicable to other elongated embayments or estuaries having a resonance period of less than 12 h, i.e., less than the period of semi-diurnal tides, typically ones with a length of 50–100 km and a depth of 15–20 m, and they can be used to assess past tidal changes as well as potential future changes. For example, a future sea-
reconstructions. In particular, we did not consider the vertical movement of seafloor caused by hydroisostatic (Okuno et al., 2014) and tectonic (Shishikura, 1999) processes because of a lack of data, which may have affected our tidal estimates. It is therefore important to understand not only the simulated features but also the mechanisms underlying them. In addition, the model formulation might have influenced the model results to some extent. Prediction of slightly smaller K1 amplitudes during 9 ka compared to those during 8 ka (by 0.02 cm; Fig. 5b) probably stem from the usage of the nonlinear bottom-drag scheme in Eq. (1), because such amplitude reduction did not occur when tides were driven solely by the K1 component. The assumption of using constant bottom drag and viscous coefficients may also have modified the result, though their influence would probably be apparent only at regions where the depth is very shallow or having a strong velocity shear, because the overall tidal pattern did not show a discernible change even when the values of cD and Ah in Eq. (1) were modified over the range of 0.015–0.035 and 20–250 m2/s, respectively. 5.3. Estuarine shrinkage We have shown that major changes in semi-diurnal tides simulated by the numerical modeling results can be explained by changes in the water depth and bay length. Here, we attempt to explain the overall
Fig. 8. Schematic image of the two types of estuarine shrinkage for two situations, i.e., Tp < Tf (a and b) and Tp > Tf (c and d), where Tp is the resonance period of the estuary and Tf is the tidal forcing period: (a and c) shrinkage associated with a reduction of bay length “l” (type-1 shrinkage) and (b and d) shrinkage of the bay relative to the length of tidal waves due to an increase in the water depth “H” or an increase in the tidal wavelength (type-2 shrinkage). The typical dimension of the Elbe estuary was taken from Winterwerp et al. (2013). Broken and solid double-ended arrows illustrate the tidal amplitudes before and after the shrinkage, respectively. (e) Overview of the two-step tidal weakening taken place in Tokyo Bay during the Holocene. Color shadings indicate predicted maximum tidal elevation, roughly half the spring tidal range, at three representative periods: the present day, 7 ka, and 9 ka. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.) 8
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level rise in such an embayment may cause a reduction of tides through type 2 estuarine shrinkage, whereas land reclamation may cause tidal weakening through type 1 shrinkage. It is to be noted that if the resonance period Tp of the estuary is (moderately) larger than the tidal period Tf, i.e., Tp > Tf, the estuarine shrinkage will act as to increase the tidal amplitude (Fig. 8c and d), an opposite sense compared to the case Tp < Tf which we have verified for the case of Tokyo Bay. Enhancement of semi-diurnal tides due to an increase in the water depth reported in several modern European estuaries (Winterwerp et al., 2013), where Tp is larger than Tf, could be recognized as a tidal enhancement due to the type 2 estuarine shrinkage (Fig. 8d).
Egbert, G.D., Ray, R.D., Bills, B.G., 2004. Numerical modeling of the global semidiurnal tide in the present day and in the last glacial maximum. J. Geophys. Res. 109, 15. https://doi.org/10.1029/2003JC001973. C03003. Endo, K., 2015. “Chuseki–so” in Japan—Latest Layer Bridging the Past and the Future. Fuzanbo International, Tokyo, pp. 416pp (in Japanese). Endo, K., Ishiwata, S., Hori, S., Nakao, Y., 2013. Tokyo Lowland and Chuseki-so: Formation of the soft ground and Jomon Transgression. J. Geogr. 122 (6), 968–991. https://doi.org/10.5026/jgeography.122.968. (in Japanese with English abstract). Endo, K., Kosugi, M., Matsushita, M., Miyachi, N., Hishida, R., Takano, T., 1989. Holocene environmental history in and around the paleo–Nagareyama Bay, central Kanto Plain. Quat. Res. (Daiyonki Kenkyu) 28 (2), 61–77. https://doi.org/10.4116/jaqua.28.61. (in Japanese with English abstract). Endo, T., 2004. Historical review of reclamation works in the Tokyo Bay area. J. Geogr. 113 (6), 785–801. https://doi.org/10.5026/jgeography.113.6_785. (in Japanese with English abstract). Esaka, T., 1972. Change of natural environment during the Jomon cultural age. Quat. Res. (Daiyonki Kenkyu) 11 (3), 135–141. https://doi.org/10.4116/jaqua.11.135. (in Japanese with English abstract). Friedrichs, C.T., 2010. Barotropic tides in channelized estuaries. In: Valle-Levinson, A. (Ed.), Contemporary Issues in Estuarine Physics Chap. 3. Cambridge University Press, Cambridge, pp. 27–61. Fujimoto, K., 1990. Reexamination of Late Holocene Sea-Level Changes in Japan 40. pp. 37–70. (2). http://hdl.handle.net/10097/45186 The science reports of the Tohoku University, 7th series (Geography). Green, J.A.M., Green, C.L., Bigg, G.R., Rippeth, T.P., Scourse, J.D., Uehara, K., 2009. Tidal mixing and the meridional overturning circulation from the last glacial maximum. Geophys. Res. Lett. 36, 5. https://doi.org/10.1029/2009GL039309. L15603. Griffiths, S.D., Hill, D.F., 2015. Tidal modeling. In: Shennan, I., Long, A.J., Horton, B.P. (Eds.), Handbook of Sea-Level Research Chap. 29. John Wiley & Sons, Ltd., Chichester. https://doi.org/10.1002/9781118452547.ch29. 438-251. Griffiths, S.D., Peltier, W.R., 2009. Modeling of polar ocean tides at the Last Glacial Maximum: amplification sensitivity, and climatological implications. J. Clim. 22 (11), 2905–2924. https://doi.org/10.1175/2008JCLI2540.1. Hill, D.F., Griffiths, S.D., Peltier, W.R., Horton, B.P., Tömqvist, T.E., 2011. High-resolution numerical modeling of tides in the Western Atlantic, Gulf of Mexico, and Caribbean Sea during the Holocene. J. Geophys. Res. 116, 16,. https://doi.org/10. 1029/2010JC006896. C10014. Hill, D.F., 2016. Spatial and temporal variability in tidal range: evidence, causes, and effects. Curr. Clim. Change Rep. 2 (4), 232–241. https://doi.org/10.1007/s40641016-0044-8. Hinton, A.C., 1997. Tidal changes. Prog. Phys. Geogr. 21 (3), 425–433. https://doi.org/ 10.1177/030913339702100306. Hori, K., Saito, Y., 2007. An early Holocene sea-level jump and delta initiation. Geophys. Res. Lett. 34, 5. https://doi.org/10.1029/2007GL031029. L18401. Hosoya, T., Onodera, S., Oshika, A., 2002. The stratigraphy and genesis of the Nakanose at the Tokyo bay. In: Proceedings of the Geological Society of Japan, vol 109. pp. 60. https://doi.org/10.14863/geosocabst.2002.0_60_2. (in Japanese). Ishihara, Y., Miyazaki, Y., Eto, C., Fukuoka, S., Kimura, K., 2013. Shallow subsurface three-dimensional geological model using borehole logs in Tokyo Bay area, central Japan. J. Geol. Soc. Jpn. 119 (8), 554–566. https://doi.org/10.5575/geosoc.2013. 0019. (in Japanese with English abstract). Ishiwata, S., 2004. The late Pleistocene-Holocene deposits and the sedimentary environment in the northern coastal area of Tokyo Bay, Central Japan. Quat. Res. (Daiyonki Kenkyu) 43 (4), 297–310. https://doi.org/10.4116/jaqua.43.297. (in Japanese with English abstract). Japan Coast Guard, 1992. Tidal Harmonic Constants Tables. Japanese Coast, Publication no. 742, Japan Coast Guard, Tokyo, pp. 257pp. Kaizuka, S., Naruse, Y., Matsuda, I., 1977. Recent formations and their basal topography in and around Tokyo bay, Central Japan. Quat. Res. 8 (1), 32–50. https://doi.org/10. 1016/0033-5894(77)90055-2. Kimura, K., Ishihara, Y., Miyachi, Y., Nakashima, R., Nakanishi, T., Nakayama, T., Hachinohe, S., 2006. Sequence stratigraphy of the latest pleistocene-holocene incised valley fills from the Tokyo and Nakagawa lowland, Kanto Plain, central Japan. Memoirs of the Geological Society of Japan 59, 1–18 (in Japanese with English abstract). Komatsubara, J., Ishihara, Y., Nakashima, R., Uchida, M., 2017. Difference in timing of maximum flooding in two adjacent lowlands in the Tokyo area caused by the difference in sediment supply rate. Quat. Int. 455, 56–69. https://doi.org/10.1016/j. quaint.2017.06.006. Kosugi, M., 1989. Coastline and adjacent environments of the former Tokyo Bay in the Holocene. Geogr. Rev. Jpn., Series A 62 (5), 359–374. https://doi.org/10.4157/ grj1984a.62.5_359. (in Japanese with English abstract). Matsuda, I., 1973. Recent deposits and buried landforms in the Tamagawa Lowland. Geogr. Rev. Jpn. 46 (5), 339–356. https://doi.org/10.4157/grj.46.339. (in Japanese with English abstract). Matsushima, Y., 1988. Relative Sea-Level Changes Obtained from Radiocarbon Ages of Molluscan Fossils: an Example from the Tama and Tsurumi River Lowlands 1. Summaries of Researches using AMS at Nagoya University, pp. 57–61 (in Japanese). Matsushima, Y., 2010. Jomon Transgression Elucidated by Fossil Molluscan Shells: World of +2°C in Southern Kanto, revised ed. Yurin Shinsho no.64, Yurindo; Yokohama, 232pp., (in Japanese). Matsushima, Y., Tanaka, G., Chiba, T., Kudo, Y., Kaneko, M., Ishikawa, H., Nomura, M., Sugihara, S., Masubuchi, K., 2016. Paleoenvironmental change of the Hirakata-wan Inlet, west of Tokyo Bay, during the Jomon Transgression. Bull. Kanagawa Prefect. Mus. Nat. Sci. 45, 1–27. (in Japanese with English abstract). http://nh.kanagawamuseum.jp/files/data/pdf/bulletin/45/bull45_01_27_matsushima.pdf.
6. Conclusions Our numerical simulation results indicate that tides in Tokyo Bay during the early to middle Holocene were stronger than those at present and that tidal conditions during these periods in the upper bay were mesotidal, mainly because of the enhancement of semi-diurnal tides, in contrast to the present microtidal setting. The maximum elevation at the bay head was 72% higher at 7 ka than it is at present, whereas tidal currents at the bay mouth were three times stronger during 9–10 ka than under present-day conditions. When tides were compared at a fixed location, tidal amplitudes were largest at 9 ka and decreased over time in two phases: from early to middle Holocene, the weakening was caused by the large rise of sea level (type 2 estuarine shrinkage), whereas from the middle to late Holocene, river delta progradation (type 1 estuarine shrinkage) was responsible for the amplitude decrease. In this study, we have introduced the concept of type 1 and type 2 estuarine shrinkage, associated with the reduction of bay length and with the increase in the water depth, respectively. It was found that estuarine shrinkage may work to weaken tides when the resonance period is shorter than the tidal forcing period (Tp < Tf), as in the case of Tokyo Bay, but it can also enhance tides when Tp > Tf as in the case of the Elbe River Estuary. Though this concept is based on a simple onedimensional resonance theory and has limitations, it may provide a useful measure to assess possible tidal changes in elongated embayments or estuaries. Declarations of interest None. Acknowledgements Authors would like to thank four anonymous reviewers for their valuable comments. This study was supported by JSPS KAKENHI Grant Number JP18K03761. References Akutsu, J., 1973. Geology of the Kawasaki to Kisarazu Subsurface Section, Central Part of Tokyo Bay, Japan, Tohoku University Scientific Report, 2nd series (Geology), Special Volume no. 6 (Hatai Memorial Volume). pp. 465–476. http://hdl.handle.net/10097/ 29004. Arbic, B., Mitrovica, J., MacAyeal, D., Milne, G., 2008. On the factors behind large Labrador Sea tides during the last glacial cycle and the potential implications for Heinrich events. Paleoceanography 23, 14. https://doi.org/10.1029/2007PA001573. PA3211. Bureau of Port and Harbor, 2001. Underground Geological Map of Tokyo Bay, 2nd ed. Tokyo Metropolitan Government, Tokyo, pp. 89 (in Japanese). Chujo, J., 1962. On the paleo–Tokyo River: prospected by the sonic prospecting. Earth Sci. (Chikyu Kagaku) 59, 30–39. https://doi.org/10.15080/agcjchikyukagaku.1962. 59_30. (in Japanese with English abstract). de Haas, T., Pierik, H.J., van der Spek, A.J.F., Cohen, K.M., van Maanen, B., 2018. Holocene evolution of tidal systems in The Netherlands: effects of rivers, coastal boundary conditions, eco-engineering species, inherited relief and human interference. Earth Sci. Rev. 177, 139–163. https://doi.org/10.1016/j.earscirev.2017.10. 006.
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of a tide-dominated incised valley during the last 14 kyr: Spatial and quantitative reconstruction in the Tokyo Lowland, central Japan. Sedimentology 62 (7), 1837–1872. https://doi.org/10.1111/sed.12204. Thomas, M., Sündermann, J., 1999. Tides and tidal torques of the world ocean since the last glacial maximum. J. Geophys. Res. 104 (C2), 3159–3183. https://doi.org/10. 1029/1998JC900097. Tojo, B., Ohno, T., Fujiwara, T., 1999. Late Pleistocene changes of tidal amplitude and phase in Osaka Bay, Japan, reconstructed from fossil records and numerical model calculations. Mar. Geol. 157 (3-4), 241–248. https://doi.org/10.1016/S00253227(98)00157-1. Toki, R., 1926. Ancient coast-line of the Kwanto Lowland with reference to its topography and the distribution of shell-mounds. Geogr. Rev. Jpn. 2 (9), 746–774. https://doi. org/10.4157/grj.2.746. (in Japanese). Uehara, K., 2005. Changes of ocean tides along Asian coasts caused by the post glacial sea-level change. In: Chen, Z., Saito, Y., Goodbred Jr.S.L. (Eds.), Mega-deltas of AsiaGeological Evolution and Human Impact. China Ocean Press, Beijing, pp. 227–232. Uehara, K., Scourse, J.D., Horsburgh, K.J., Lambeck, K., Purcell, A.P., 2006. Tidal evolution of the northwest European shelf seas from the Last Glacial Maximum to the present. J. Geophys. Res. Ocean. 111, 15. https://doi.org/10.1029/2006JC003531. C0925. Umitsu, M., 1991. Holocene sea-level changes and coastal evolution in Japan. Quat. Res. (Daiyonki Kenkyu) 30 (2), 187–196. https://doi.org/10.4116/jaqua.30.187. Unoki, S., 1993. Physical Oceanography in Coastal Area. Tokai University Press, Tokyo, pp. 672pp (in Japanese). Walker, M., Head, M.J., Berkelhammer, M., Björck, S., Cheng, H., Cwynar, L., Fisher, D., Gkinis, V., Long, A., Lowe, J., Newnham, R., Rasmussen, S.O., Weiss, H., 2018. Formal ratification of the subdivision of the Holocene series/epoch (quaternary system/period): two new global boundary stratotype sections and points (GSSPs) and three new stages/subseries. Episodes 41 (4), 213–223. https://doi.org/10.18814/ epiiugs/2018/018016. Ward, S.L., Neill, S.P., Scourse, J.D., Bradley, S.L., Uehara, K., 2016. Sensitivity of palaeotidal models of the northwest European shelf seas to glacial isostatic adjustment since the last glacial maximum. Quat. Sci. Rev. 151, 198–211. https://doi.org/10. 1016/j.quascirev.2016.08.034. Winterwerp, J.C., Wang, Z.B., van Braeckel, A., van Holland, G., Kösters, F., 2013. Maninduced regime shifts in small estuaries–II: a comparison of rivers. Ocean Dynam. 63 (11–12), 1293–1306. https://doi.org/10.1007/s10236-013-0663-8. Yanagi, T., Ohnishi, K., 1999. Change of tide, tidal current, and sediment due to reclamation in Tokyo Bay. Umi no Kenkyu 8 (6), 411–415. https://doi.org/10.5928/ kaiyou.8.411. (in Japanese with English abstract).
Miles, J., Munk, W., 1961. Harbor paradox. J. Waterways Harb. Div., Am. Soc. Civ. Eng. 87 (3), 111–132. Okuno, J., Nakada, M., Ishii, M., Miura, H., 2014. Vertical tectonic crustal movements along the Japanese coastlines inferred from the late Quaternary and recent relative sea-level changes. Quat. Sci. Rev. 91, 42–61. https://doi.org/10.1016/j.quascirev. 2014.03.010. Pelling, H.E., Uehara, K., Green, J.A.M., 2013. The impact of rapid coastline changes and sea level rise on the tides in the Bohai Sea, China. J. Geophys. Res. Oceans 118, 11. https://doi.org/10.1002/jgrc.20258. Peltier, W.R., 2004. Global glacial isostasy and the surface of the ice-age earth: the ICE-5G (VM2) model and GRACE. Annu. Rev. Earth Planet Sci. 32 (1), 111–149. https://doi. org/10.1146/annurev.earth.32.082503.144359. Peltier, W.R., Argus, D.F., Drummond, R., 2015. Space geodesy constrains ice-age terminal deglaciation: The global ICE-6G_C (VM5a) model. J. Geophys. Res. Solid Earth 120, 450–487. https://doi.org/10.1002/2014JB011176. Pickering, M.D., Horsburgh, K.J., Blundell, J.R., Hirschi, J.J.-M., Nicholls, R.J., Verlaan, M., Wells, N.C., 2017. The impact of future sea-level rise on the global tides. Cont. Shelf Res. 142, 50–68. https://doi.org/10.1016/j.csr.2017.02.004. Saito, Y., 1995. High-resolution sequence stratigraphy of an incised-valley fill in a waveand fluvial-dominated setting: latest Pleistocene-Holocene examples from the Kanto Plain, central Japan. Mem. Geol. Soc. Jpn. 45, 76–100. http://dl.ndl.go.jp/ info:ndljp/pid/10810120. Saito, Y., Kayanne, H., 1991. Coastal evolution and changes in relation to eustatic sealevel changes, tectonics and human activity, Futtsu cuspate foreland of Tokyo Bay, central Japan. J. Sedimentol. Soc. Jpn. 34, 135–138. https://doi.org/10.14860/ jssj1972.34.135. (in Japanese). Schindelegger, M., Green, J.A.M., Wilmes, S.-B., Haigh, I.D., 2018. Can we model the effect of observed sea level rise on tides? J. Geophys. Res. Oceans 123, 4593–4609. https://doi.org/10.1029/2018JC013959. Shirai, S., Tomidokoro, T., Noguchi, K., 2004. Overview on Tokyo Bay undersea gas pipeline for connecting east and west. Elect. Power Civ. Eng. 313, 51–55 (in Japanese). Shishikura, M., 1999. Holocene marine terraces and seismic crustal movements in Hota Lowland in the southern part of Boso Peninsula, Central Japan. Quat. Res. (Daiyonki Kenkyu) 38 (1), 17–28. https://doi.org/10.4116/jaqua.38.17. (in Japanese with English abstract). Tanabe, S., Ishihara, Y., Nakanishi, T., 2010. Stratigraphy and physical property of the alluvium under the Tokyo and Nakagawa Lowlands, Kanto Plain, central Japan: implications for the alluvium subdivision. J. Geol. Soc. Jpn. 116 (2), 85–98. https:// doi.org/10.5575/geosoc.116.85. (in Japanese with English abstract). Tanabe, S., Nakanishi, T., Ishihara, Y., Nakashima, R., 2015. Millennial-scale stratigraphy
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Tidal amplitude decreases in response to estuarine shrinkage: Tokyo Bay during the Holocene
T
Katsuto Ueharaa,∗, Yoshiki Saitob,c a
Research Institute for Applied Mechanics, Kyushu University, 6-1 Kasuga Koen, Kasuga, Fukuoka, 816-8580, Japan Estuary Research Center, Shimane University, 1060 Nishikawatsu-cho, Matsue, Shimane, 690-8504, Japan c Geological Survey of Japan, AIST, 1-1-1 Higashi, Tsukuba, Ibaraki, 305-8567, Japan b
A R T I C LE I N FO
A B S T R A C T
Keywords: Estuaries Tides Sea level changes Palaeoclimate Tidal resonance
Tidal changes in Tokyo Bay during the last 10,000 years were investigated by combining a numerical model with newly compiled model bathymetries for the present day, the early 20th century, and every 1000 years from 4000 to 10,000 years ago. Over this time period, sea level has changed by more than 30 m, and the coastline has shifted 50–60 km. Tides during the early 20th century and 4000–9000 years ago were larger than those at present; from 9000 to 4000 years ago, the bay setting was mesotidal, in contrast to the modern microtidal setting. The maximum tidal level at the head of the bay was 72% higher 7000 years ago than at present, and M2 tidal currents at the bay mouth from 10,000 to 9000 years ago were three times stronger than those at present. When tides were compared at a fixed location, the greatest tidal enhancement was found to have occurred 9000 years ago. The weakening of tides over the last 9000 years can be explained by introducing the concept of estuarine shrinkage together with quarter-wavelength resonance theory. Tidal weakening occurred in two phases: during the first phase, 9000–7000 years ago, it was due to the rise in sea level (type 2 shrinkage), and during the second phase, a decrease in the length of the bay was responsible (type 1 shrinkage). These findings can be applied to the assessment of both past tidal changes and potential future tidal changes in other elongated estuaries with lengths of several tens of kilometers.
1. Introduction Many estuaries and embayments in East and Southeast Asia have experienced extensive coastline changes since about 20,000 years ago (20 ka), the time of the last glacial maximum (LGM). From the LGM to the mid-Holocene (where the Holocene encompasses the last 11.7 × 103 years or 11.7 kyr; Walker et al., 2018), a sea-level rise of more than 100 m along receding coastlines led to the formation of drowned valleys. Subsequently, during the middle to late Holocene, when sea level remained stable or fell by several meters, these valleys became filled with sediment and the coastline shifted seaward (Umitsu, 1991; Hori and Saito, 2007; Endo, 2015). Among embayments in Japan, Tokyo Bay (Fig. 1) is one of those where the millennium-scale coastline changes were first investigated (e.g. Toki, 1926). It is estimated that during the period of maximum transgression in the mid-Holocene, the landward retreat of the coastline by more than 60 km relative to its current position led to the formation of an inner bay called Oku (or Upper) Tokyo Bay (Kaizuka et al., 1977). Tidal characteristics in estuaries and embayments depend primarily
∗
on the embayment shape, and they are therefore susceptible to changes in coastlines and sea level (Pickering et al., 2017; de Haas et al., 2018; Schindelegger et al., 2018). Thus, tides in Tokyo Bay are expected to have experienced large modifications during the Holocene. Fujimoto (1990) developed a linear analytical model for Tokyo Bay in the midHolocene and inferred that the tidal range exceeded 7 m at maximum transgression, more than four times the present tidal range. Although this mid-Holocene tidal enhancement is plausible (indeed, it is confirmed in the current study), the model seems to have overestimated the tidal range, probably because, in this pioneering work, Fujimoto (1990) assumed frictionless and uniform-depth settings and also because the obtained result was beyond the applicable range of the linear theory. Since the 1980s, a number of tidal simulations have been carried out to reconstruct Holocene tides in various oceans and coastal seas around the world (for reviews see Hinton, 1997; Griffiths and Hill, 2015; Ward et al., 2016). These studies suggest that, during the early Holocene, semi-diurnal tides were enhanced especially in the North Atlantic Ocean (e.g., Thomas and Sündermann, 1999; Egbert et al., 2004; Uehara et al., 2006; Arbic et al., 2008; Green et al., 2009; Hill et al.,
Corresponding author. E-mail address: [email protected] (K. Uehara).
https://doi.org/10.1016/j.ecss.2019.05.007 Received 7 September 2018; Received in revised form 26 April 2019; Accepted 18 May 2019 Available online 20 May 2019 0272-7714/ © 2019 Elsevier Ltd. All rights reserved.
Estuarine, Coastal and Shelf Science 225 (2019) 106225
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Fig. 1. (a) Map of the study area. Red lines denote the location of sections shown in Fig. 5; the solid line follows the paths of the Ko (Paleo) Tokyo River and the paleo–Naka River whereas the broken line is aligned with the axis of the modern bay. Black dotted lines indicate the maximum extent of the Holocene transgression (cf. Kosugi, 1989) and blue solid lines indicate the position of major river channels. Symbols in diamond indicate the location of tide-gauges—MK: Makuchi, YS: Yokosuka, YH: Yokohama (Shinko), HM: Harumi, CL: Chiba Light. Other abbreviated features represent AL: Arakawa Lowland, NL: Nakagawa Lowland, TL: Tokyo Lowland, KS: Kawasaki, NS: Nakanose Shoal, FS: Futtsu Spit, CK: Cape Kannon. Two black broken lines denote the location of the northern and southern limit of the Uraga Strait. (b) Map of the model domain. Color shadings show geological structures according to land-usage maps issued by Geographic Institute of Japan. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)
rectangle about 60 km long and 20 km wide (Fig. 1a). Though the bay's average depth is about 18 m, a submarine channel with a water depth greater than 40 m is developed along the western side of the bay south of 35.4°N. The channel deepens to about 70 m at the bay mouth and becomes as deep as 700 m at the southern end of the Uraga Strait, at about 35.05°N. To the east of this channel, an isolated mound called the Nakanose Shoal is separated from coastal shoals by narrow channels on its eastern and western sides (Fig. 1a). The shoal, which consists of consolidated sediments of mid-Pleistocene age, is at a water depth of 13–17 m (Hosoya et al., 2002). A remnant of the channel developed during the last glacial sea-level lowstand, when most of the modern bay area was exposed subaerially, can be traced northward along the western side of the modern bay. This largely buried channel is called the Ko (or Paleo) Tokyo River (Chujo, 1962). During the lowstand, fluvial processes eroded Pleistocene terraces that had formed during the last interglacial (ca. 120 ka), and rivers flowed in incised valleys into the Ko Tokyo River. From the latest Pleistocene to the mid-Holocene, sea level rose rapidly, and seawater filled these valleys (Kaizuka et al., 1977). This transgression, called Jomon Kaishin, was most extensive on the northwestern side of the modern bay, where submergence of the paleo–Arakawa (Ara River) and paleo–Nakagawa (Naka River) valleys formed an inner bay called Oku Tokyo Bay (Fig. 1b). Sea level at the time of maximum transgression has been estimated to have been several meters higher than the present sea level (Umitsu, 1991), and Oku Tokyo Bay may have been as long as 50–60 km (Esaka, 1972; Kosugi, 1989). Since the mid-Holocene, sea level has remained stable or has fallen by several meters, and progradation of the river deltas has shifted the coastline to its present position. The modern lowlands (Fig. 1b) formed by the filling of the incised valleys with sediments; the Nakagawa, Arakawa, and Tokyo lowlands, have elevations of less than 5–7 m above mean sea level (Tanabe et al., 2015). The fine, soft sediments that filled the incised valleys during the latest Pleistocene and Holocene are known as the Chusekiso layer. They have a maximum thickness of more than 70 m in the relict valley of the Ko Tokyo River (Endo, 2015). In the northern part of the modern Tokyo Bay, the Chusekiso layer has been divided into two sublayers. The lower fluvial deposits (Nanagochi Formation) were deposited during the latest Pleistocene, and the upper marine deposits (Yurakucho Formation)
2011) and diurnal tides in the South China Sea (Uehara, 2005; Griffiths and Peltier, 2009). Arbic et al. (2008) and Hill (2016) describe the basic concepts of such simulations. To date, however, the only numerical attempt to reconstruct paleotides in Japanese coastal waters is that by Tojo et al. (1999), who used a one-dimensional numerical model to correlate the growth pattern of fossil bivalve shells with paleotides in Osaka Bay. The estimation of paleotides in Japanese embayments is hindered primarily by the presence of thick Holocene deposits filling the relict valleys; these deposits make it difficult to reconstruct paleodepths during specific time periods. In the last decade, however, sequencestratigraphy models applied to the lowlands north of modern Tokyo Bay, a major depocenter, have provided detailed three-dimensional paleodepth information (e.g. Tanabe et al., 2015). The objectives of this study were twofold. First, to provide basic information on paleotides in Tokyo Bay during the last 10 kyr, when seawater filled the main portion of the bay. Second, to examine the basic mechanisms of tidal changes in estuaries and embayments having a spatial scale of tens of kilometers to assess how modifications of sea level and coastlines can alter tidal features. This study is a first attempt to use a two-dimensional model to estimate changes in paleotides in Japanese embayments. To accomplish these objectives, we prepared high-resolution paleobathymetries incorporating the latest information on Holocene sediments in the Tokyo Bay area, one of the most densely investigated regions of Japan. 2. Regional setting Tokyo Bay, central Japan, is bounded by the Kanto Plain on the north, the Miura Peninsula on the southwest, and the Boso Peninsula on the southeast; on the south, it is connected to the Pacific Ocean via the Uraga Strait (Fig. 1). The offshore boundary of the modern bay is commonly considered to be the northern end of the Uraga Strait, along a line connecting Cape Kannon and Futtsu Spit, where oceanic ecological and hydrographic features switch to inner-bay conditions. In this study, however, we defined the bay area as the entire embayment north of 35.25°N, the latitude of Cape Kannon, because Futtsu Spit did not exist during the early to middle Holocene. The modern bay can be approximated by a northeastward-tilted 2
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Because the present-day bathymetry includes artificial features such as reclaimed land and dredged channels, we reconstructed the bathymetry during the 1920s–1930s (referred to hereafter as the “early 20th century” or “1930″ bathymetry) by referring to navigational charts issued from 1924 to 1936 (Fig. 2b). Although the area of the bay during that period was 28% larger than at present, its average depth was lower by 18% because of the presence of shoals developed along the northern coast. We used this bathymetry as a reference in our compilations of paleobathymetry data.
were deposited mainly during the Holocene (Tanabe et al., 2010). The Yurakucho Formation is often further subdivided into lower and upper units, which are considered to have been deposited during the retreat and advance of the shoreline, respectively (Ishiwata, 2004). Most of the coastline north of 35.33°N has been modified by human activities such as land reclamations and seawall constructions, mainly during the 1960s and 1970s (Endo, 2004). In the northeastern and eastern parts of the bay, a pre-Holocene basal platform extends seaward from the coast; this platform, which formed by wave action, is buried at water depths of 10–20 m (Kaizuka et al., 1977).
3.2. Paleobathymetries
3. Methods
Paleobathymetries from 10 ka to 4 ka (Fig. 2c–i) were reconstructed by referring to multiple sources, as outlined below. The dataset was newly compiled because no comprehensive dataset covering Tokyo Bay as a whole existed. The compiled dataset incorporates outcomes of sequence-stratigraphy models that include detailed isochrones for the Holocene layers for three regions: the Nakagawa and Tokyo lowlands south of 36°N (Kimura et al., 2006; Tanabe et al., 2015), the Arakawa Lowland (Komatsubara et al., 2017), and the Obitsu River delta (Saito, 1995). We referred to geological cross sections to reconstruct bathymetries of the northwest coast of the modern bay (Bureau of Port and Harbor, 2001; Ishiwata, 2004; Ishihara et al., 2013), the Tama River delta (Matsuda, 1973; Matsushima, 1988), the Yokohama area (Matsushima, 2010), the Yokosuka area (Matsushima et al., 2016), and the Futtsu Spit (Saito and Kayanne, 1991), and we also used two sections transecting the bay at about 35.3°–35.5°N (Akutsu, 1973; Shirai et al., 2004). Where date information was not available in the geological records, the boundary between the Nanagochi and Yurakucho formations was
Paleotides were reconstructed using a two-dimensional tidal model based on paleobathymetry data for specified times, namely, two times in the modern era when Oku Tokyo Bay was not extant (the present day and early 20th century), and every 1 kyr from 4 ka to 10 ka, when a marine environment prevailed in Oku Tokyo Bay, north of the modern bay. All dates in this study are presented as calibrated years. 3.1. Modern bathymetries Bathymetric data used for tidal reconstruction were defined on a longitude–latitude grid covering longitudes from 139.51°E to 140.17°E and latitudes from 35.15°N to 36.24°N with a resolution of 0.01° (ca. 1 km). For the present-day bathymetry of Tokyo Bay (Fig. 2a), we compiled data from electronic navigational charts issued in 2014 (in Figs. 2–6, results based on this bathymetry are labeled as “2014″). Water depths obtained from the charts were raised by 1 m to correct for the difference between mean sea level and the chart datum.
Fig. 2. Model bathymetries used in this study. Light and dark gray shadings indicate areas having elevation of 10–15 m and over 15 m relative to the modern sea level, respectively. The depths are measured downward from the mean sea level at each time slice. 3
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Fig. 3. Horizontal distribution of the maximum elevation predicted by the numerical model. The contour interval is 0.05 m.
∂η/∂t + ∇·U = 0,
correlated with the base of the Holocene, and the boundary between the upper and lower units of the Yurakucho Formation was considered to approximately coincide with the maximum transgression. In areas where detailed geological information was not available, we used the depth of the base of the Chusekiso layer to constrain the lower limit of Holocene sediments. For this purpose, we referred to several maps (e.g. Kaizuka et al., 1977; Endo et al., 2013) and to Submarine Geological Structural Charts issued by the Japan Coast Guard showing the depth of the layer's base. Where the present-day sea is deeper than 10–20 m, the reconstructed paleodepths include large uncertainties because, aside from the two submarine sections mentioned above, the depth of the Chusekiso layer base was the only information available. In this study, following Tanabe et al. (2015), we assumed that the maximum transgression occurred at 7 ka, except in the paleo–Arakawa Valley, where the coastline started to advance seaward at 8 ka (Komatsubara et al., 2017). We adopted the sea-level curve of Tanabe et al. (2015), as modified from that of Endo et al. (1989), to determine paleodepths. Relative to the present, sea level was assumed to be −30 m at 10 ka, −17 m at 9 ka, −5 m at 8 ka, +3 m during 7–6 ka, +1 m at 5 ka, and the same as present during the last 4 kyr.
where U = Du, u the horizontal current vector, D = H + η the thickness of the vertical column, H the undisturbed depth, η the surface elevation relative to mean sea level, f the Coriolis parameter, k the unit vertical vector, × the vector cross product, g the gravitational acceleration (=9.806 m/s2), ∇ the horizontal gradient operator, cD the bottom drag coefficient (= 0.0025), and Ah the horizontal viscosity coefficient (= 100 m2/s). We adopted the numerical scheme of Pelling et al. (2013) to handle tides in intertidal zones. Each experiment was conducted on a 0.01° × 0.01° grid for 45 days from rest, and the last 29.53 days (a synodic month) were used for the analysis. The same model settings, except for the bathymetry, were used for all experiments. In the model, tides are driven by specifying the surface elevation along the offshore open boundary. This boundary value was compiled from the harmonic constants of four major tidal components recorded at the Makuti tide-gauge station (amplitudes 37.3 cm, 16.8 cm, 22.9 cm, and 19.7 cm for M2, S2, K1, and O1 tides, respectively; Japan Coast Guard, 1992). The discrepancy between the observed and simulated present-day tides at the four tide-gauge stations, Chiba-light, Tokyo (Harumi), Yokohama (Shinko), and Yokosuka, was 1.6 cm (root-meansquare difference) or 3.5% (mean relative deviation) in the case of the M2 amplitude and 1.8° (root-mean-square difference) in the case of the M2 phase. Because this discrepancy in tidal amplitude is close to the resolution of the sea-level measurements (1 cm) and smaller than the difference in the maximum tidal amplitude between the present-day and early 20th century cases (ca. 4 cm; section 4), we consider the accuracy of the model to be sufficient to resolve tidal changes in the study area. In this study, the tides at the offshore open boundary were assumed
3.3. Tidal model We introduced a two-dimensional tidal model based on Uehara et al. (2006) and Pelling et al. (2013) to estimate present-day and past tides and tidal currents. The model formulations and range of parameters adopted are comparable to those commonly used for tidal models of present-day coastal seas: ∂U/∂t + (u·∇)U - f k × U = - gD∇ η - cD|u|u + Ah∇·(D∇u),
(2)
(1) 4
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Fig. 4. Horizontal distribution of M2 velocity amplitudes predicted by the numerical model.
Fig. 5. (a) Changes in the maximum elevation along a section aligned with the axis of the modern bay (cases 2014 and 1930; red dashed line in Fig. 1a) or with that of the paleo-bay (other cases; red solid line in Fig. 1a). (b) Same as Fig. 5a except for M2 and K1 amplitudes and that values in intertidal zones are not shown. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)
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4.1.2. Harmonic constants At each time slice, the horizontal pattern of the amplitudes of the four major tidal constituents was similar to that of the maximum elevations shown in Fig. 3, except that the amplitudes were small in intertidal areas (not shown). The tidal amplitudes increased toward the bay head and across-axis variations were small. Tidal phases lagged toward the bay head; for diurnal tides, the lag in the interior region north of about 35.4°N was about 5°, and for semi-diurnal tides it was 10°. In addition, phases were advanced by 1°–2° on the eastern side compared to the western side of the bay. This east-west tidal-phase asymmetry was not apparent in test runs conducted without taking account of the Coriolis force, so the asymmetry is likely due to the Coriolis effect. 4.1.3. M2 tidal velocity Fig. 4 illustrates the horizontal distribution of M2 tidal current amplitudes, the strongest tidal component in the study area. Most of the simulated tidal current ellipses were rectilinear (unidirectional) and aligned parallel to the bay axis, so only the amplitudes are shown in the figure. At all time slices, the strongest M2 tidal current was observed around the bay mouth; the speed was 0.33 m/s in the present-day case, 0.45 m/s during the early 20th century, 0.7–0.8 m/s during 4–7 ka, and 0.9–1.0 m/s at 8 ka and earlier. These results indicate that the maximum M2 current was about three times stronger during the early Holocene than it is at present and that the maximum current speed has decreased over time. During 6–8 ka, the bay mouth was wider than at present because Futtsu Spit did not yet exist. Additional test runs with paleobathymetries modified to include Futtsu Spit showed that when the bay mouth was wider (i.e., simulations without the spit), the tidal current around the bay mouth was weaker than in simulations with the spit. Strong tidal currents were distributed mainly in three areas: the bay mouth region south of about 35.4°N, a constricted area north of the modern bay, and the northern part of the paleo–Nakagawa Valley. The locations of intense tidal currents at each time slice did not differ greatly between diurnal and semi-diurnal tides; this result suggests that the position of energetic currents was controlled mainly by local topographic conditions rather than by basin-wide tidal dynamics. East of 139.95° E, M2 tidal currents were weaker than 0.1 m/s from 8 ka. This result indicates that the influence of tidal currents in northeastern and eastern part of the modern bay has been small since 8 ka, and is consistent with previous findings based on geomorphological analyses that erosional features such as the submarine terraces found in this area were formed by wave actions (Kaizuka et al., 1977). At all time slices, the phase difference between the tidal elevation and the tidal current was 80°–90° in most regions (not shown); this result suggests that the tidal waves in the bay behaved as standing waves, not as progressive waves.
Fig. 6. Tidal response curves at different time slices as a function of the tidal forcing period. Two vertical gray lines denote the period of M2 and K1 tides.
to be the same as at present in all cases for two reasons. First, global paleo-ocean tide simulations indicate that tidal changes in the northwest Pacific Ocean have been small during the last 20 kyr (e.g. Egbert et al., 2004; Uehara et al., 2006; Griffiths and Peltier, 2009). Second, relative sea levels reconstructed by the latest glacial isostatic models show large discrepancies around the study area (e.g. about −10 m at 10 ka; Peltier, 2004; Peltier et al., 2015) with those reconstructed by using local proxy records (e.g. −30 to −40 m at 10 ka; Endo, 2015; Tanabe et al., 2015). Because at present the performance of global paleo-ocean tide models depends greatly on the output of isostatic models, it was not possible to retrieve open-boundary values from global paleotidal models that were consistent with the paleobathymetries determined by using local geological records.
4. Results 4.1. Horizontal distributions 4.1.1. Maximum tidal elevations Numerical simulation shows the horizontal distribution of maximum tidal elevations, i.e. the highest tidal elevation in a synodic month (29.53 days); this includes the contribution of compound tides, which was large in intertidal zones (Fig. 3). In the case of present-day Tokyo Bay, the simulated maximum elevation is comparable to the mean high water spring (MHWS) or half the spring tidal range. For example, MHWS computed from the tide-gauge record at the Chibalight station from 1995 to 2013, 0.74 m, is comparable to the modelsimulated maximum elevation of 0.77 m. At all time slices, the maximum elevation increased toward the bay head along a line parallel to the bay axis, whereas the across-axis variation was small. In the area occupied by the present-day bay, the maximum elevations during 4–9 ka were higher than those at present. Tidal elevations during the early 20th century were also higher than those at present, consistent with the numerical study results for M2 tides reported by Yanagi and Ohnishi (1999). Although the maximum elevation was highest in the northeastern corner of the bay during the modern eras (Fig. 3a and b), the highest values at 4 ka and before were observed at the head of the paleo–Nakagawa Valley. An exception was at 8 ka (Fig. 3g) when the paleo–Arakawa Valley was most extensive. The maximum elevation was slightly higher at the head of the paleo–Arakawa Valley than at the head of the paleo–Nakagawa Valley. During 9–7 ka, maximum elevations at the paleo–bay head exceeded 1.25 m, and during 6–4 ka, they exceeded 1.1 m.
4.2. Along-axis profiles To examine the tidal changes in more detail, we constructed profiles of the maximum levels and amplitudes of the M2 and K1 tidal constituents along sections parallel to the bay axis (Fig. 5). The section for 4–10 ka follows the paths of the Ko Tokyo River and the paleo–Naka River, and the section for the two modern periods is aligned with the axis of the modern bay north of 35.5°N (see Fig. 1a). The amplitudes of the S2 and O1 tidal constituents are not shown, but their profiles were similar to those of the M2 and K1 constituents, respectively. The maximum elevation increased monotonically toward the bay head, except at 10 ka, when the elevation decreased slightly near the bay mouth (Fig. 5a). The highest maximum elevation of 1.34 m, which was observed at 7 ka, is about 72% larger than that at present. The maximum elevation was higher than 1 m along the section north of 35.7°N during 4–9 ka and around the bay head at 10 ka. Because the 6
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the M2 constituent and 12 h for the S2 constituent), and the resonance period basically became shorter over time. During 9–10 ka, the tidal response peaks were smaller and broader compared with those for the other time slices. These peak characteristics are attributable to a higher level of dissipation caused by the narrow configuration of the bay and shallow water depths during these time slices. The major features of the observed tidal changes can be explained by the changes in the resonance period. The most enhanced semidiurnal tides emerged during the early Holocene, when the resonance period was closest to the semi-diurnal period. Over time the resonance became shorter, and the difference between the resonance period and the semi-diurnal period increased. The greatest enhancement of the semi-diurnal tides was observed at 9 ka, probably because the bay at 10 ka was shallow (the average depth about 9 m) and narrow and the influence of friction was large, as was suggested by a broad and less distinctive peak feature of the response curve for 10 ka (Fig. 6). The invariable nature of the diurnal tides in terms of both time and space can be attributed to the fact that the forcing period differed greatly from the resonance period. As a result, the tidal response was less sensitive to shifts in the resonance period.
maximum elevation is comparable to MHWS or half the mean spring tidal range (see section 4.1.1), the spring-tide condition in the upper bay during 4–10 ka must have been mesotidal (tidal range 2–4 m), different from the microtidal (tidal range less than 2 m) condition at present. When tides were compared at a fixed location, the maximum elevation was found to be highest at 9 ka along the main part of the section north of the channel adjacent to the Nakanose Shoal at about 35.45°N. Similar to their maximum elevations, amplitudes of the M2 and K1 tidal constituents increased toward the head of the bay (Fig. 5b), except in intertidal zones, where amplitudes of major tidal constituents were small because the lower limit of low tide levels was suppressed by the presence of tidal flats (not shown). Tidal amplitudes within the bay behaved quite differently between semi-diurnal (M2 constituent in Fig. 5b) and diurnal (K1 constituent) tides in terms of both space and time. At all time slices, changes in tidal amplitudes toward the bay head were more evident for M2 tides than for K1 tides. In addition, the ratio of the M2 amplitude at the bay head to that at the bay mouth (both measured along the section) decreased greatly over time, from 2.1 at 9 ka to 1.2 at present, in contrast to that of the K1 amplitude, which remained around 1.1 at all time slices. This result indicates that the past enhancement of tides was due mainly to the greater development of the semi-diurnal tides. For example, 93% of the difference in the highest maximum elevation between 9 ka (at 36°N, south of the intertidal zone) and the present can be explained by the amplitude change of the M2 and S2 tides between those two time slices. As a result, the contribution of semi-diurnal tides to maximum elevations in the upper bay was higher prior to 4 ka than at present. In the present-day case, the ratio of diurnal (K1 and O1) to semi-diurnal (M2 and S2) tides decreased from 0.79 at the offshore model boundary to 0.63 at the head of the bay. At 9 ka, the ratio at the bay head further decreased to 0.42. Thus, semi-diurnal tides were more dominant during the early to middle Holocene than at present. In contrast to the pattern in maximum elevation (Fig. 5a), the largest M2 amplitude was lower at 7 ka than during 9–8 ka, even though the area of the bay was largest at 7 ka (Fig. 5b). When tides were observed at a fixed location, the M2 amplitude, like its maximum elevation, was largest at 9 ka in the interior region north of about 35.45°N but decreases in the M2 amplitude did not occur uniformly through time (Fig. 5b). For example, the smallest M2 amplitudes during 9–4 ka were observed at 6 ka along the section north of 35.4°N.
5.2. Impact of bay length and water depth The basic process leading to shifts of the resonance period can be explained by simple quarter-wavelength resonance theory, which relates the resonance period Tp of a one-dimensional, constant-depth frictionless channel to the channel length l and the mean water depth H
Tp = 4l/ gH
(3)
Although this theory does not take account of effects such as friction, radiation damping (Miles and Munk, 1961), and changes in the depth and width of a bay (Friedrichs, 2010), the simulated paleotides in Tokyo Bay fulfill the background assumption that the tide behaves as a standing wave, and its amplitude increases monotonically toward the bay head. In the case of Tokyo Bay, where the resonance period was found to be shorter than semi-diurnal tidal periods, diurnal and semi-diurnal tides are expected to become weaker as the resonance period Tp becomes shorter. According to Eq. (3), if the water depth increases or the length of the bay decreases, the resonance period will become shorter. We confirmed this relationship by conducting additional experiments for 7 ka in which the water depth was decreased by 1 m or the northern end of the bay was truncated. Tidal changes associated with the shift of resonance period were caused by the combined effects of variation in depth and length. Our results indicate that the simulated decrease in M2 amplitudes from 9 to 7 ka was caused primarily by the effect of the depth increase associated with a large sea-level rise, which seems to have overcome the effect of tidal strengthening due to the increase in the bay length. Further weakening of M2 tides from 7 to 6 ka, during the initial phase of delta progradation at the bay head (Fig. 7a), was caused mainly by the truncation of the bay length. The slight increase in tidal amplitudes during 6–5 ka and 5–4 ka, when the sea level was inferred to have dropped by 2 m and 1 m, respectively, was due mainly to the shoaling of the bay caused by the sea-level change and also by infilling of the incised valleys in Oku Tokyo Bay (Fig. 7b and c). The infilling might have contributed more to the shoaling of the bay than the sea level change, because the tidal enhancement was more apparent within Oku Tokyo Bay north of 35.7°N (Fig. 5b). Finally, the large decrease in tidal amplitudes during the last 4 kyr can be explained by the truncation of the bay length caused by river delta progradation. While the enhanced tides simulated during 9–4 ka seem to represent a robust feature, the detailed pattern of the estimated tidal changes, such as the slightly enhanced tidal amplitudes during 5 ka and 4 ka, might be modified in the future by more refined paleotopographic
5. Discussion 5.1. Shift of the resonance period As shown in section 4.2, temporal changes in the M2 amplitude were not directly linked to changes in the area occupied by the bay. The amplitudes were largest at 9 ka, decreased over time until 6 ka, and then increased slightly during 5–4 ka (Fig. 5b), even though the bay area was largest at 7 ka. Here, we examine the sensitivities of tidal amplitudes to sea level and water depth in relation to shifts in the resonance period of the bay. First, we estimated tidal response curves as a function of the tidal forcing period so that we could numerically infer the resonance period of the bay at different time slices (Fig. 6). The curves were drawn by conducting a series of numerical runs in which tides forced by water levels at the open boundary oscillated with an amplitude of 37.3 cm in a single period ranging between 2.4 and 26 h. The largest tidal amplitude observed in each run was then plotted. The tidal period resulting in the maximum tidal response was about 6.0 h for the present-day setting, which is consistent with the observed resonance period of the bay at present (Unoki, 1993), and it was 6.8 h for the early 20th century case, around 8 h during 4–7 ka, 8.6 h at 8 ka, 10 h at 9 ka, and 12 h at 10 ka. Thus, the resonance period of Tokyo Bay during the last 10 kyr was comparable or shorter than the semi-diurnal tidal period (12.42 h for 7
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Fig. 7. Depth changes taken place in (a) 7–6 ka, (b) 6–5 ka, and (c) 5–4 ka, when the bay become smaller in area and shallower in depth. The difference presented in color shadings are drawn only on the sea area at the newer age. Thick lines denote the coastline at the older age. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)
decrease of tides since the early Holocene by introducing the concept of estuarine shrinkage. From the middle to late Holocene, delta progradation truncated the bay, and the shorter bay length worked to weaken the tides. We refer to a reduction of bay length leading to tidal weakening as type 1 estuarine shrinkage (Fig. 8a). The weakening of tides from the early to middle Holocene, caused by the increase in water depth associated with the sea-level rise, can also be regarded as due to shrinkage of the embayment relative to the length of the tidal waves, because tidal wavelength is proportional to the square of water depth and thus increases when the water depth increases. Therefore, we call shrinkage due to a sealevel rise accompanied by tidal weakening as type 2 estuarine shrinkage (Fig. 8b). To summarize, the overall decrease in tidal amplitudes during the last 9 kyr occurred in two phases by different mechanisms: during the first phase, type 2 estuarine shrinkage was caused by the large sea-level rise during the early to middle Holocene, and it was succeeded during the second phase by type 1 estuarine shrinkage caused by river delta progradation (Fig. 8e). These mechanisms are applicable to other elongated embayments or estuaries having a resonance period of less than 12 h, i.e., less than the period of semi-diurnal tides, typically ones with a length of 50–100 km and a depth of 15–20 m, and they can be used to assess past tidal changes as well as potential future changes. For example, a future sea-
reconstructions. In particular, we did not consider the vertical movement of seafloor caused by hydroisostatic (Okuno et al., 2014) and tectonic (Shishikura, 1999) processes because of a lack of data, which may have affected our tidal estimates. It is therefore important to understand not only the simulated features but also the mechanisms underlying them. In addition, the model formulation might have influenced the model results to some extent. Prediction of slightly smaller K1 amplitudes during 9 ka compared to those during 8 ka (by 0.02 cm; Fig. 5b) probably stem from the usage of the nonlinear bottom-drag scheme in Eq. (1), because such amplitude reduction did not occur when tides were driven solely by the K1 component. The assumption of using constant bottom drag and viscous coefficients may also have modified the result, though their influence would probably be apparent only at regions where the depth is very shallow or having a strong velocity shear, because the overall tidal pattern did not show a discernible change even when the values of cD and Ah in Eq. (1) were modified over the range of 0.015–0.035 and 20–250 m2/s, respectively. 5.3. Estuarine shrinkage We have shown that major changes in semi-diurnal tides simulated by the numerical modeling results can be explained by changes in the water depth and bay length. Here, we attempt to explain the overall
Fig. 8. Schematic image of the two types of estuarine shrinkage for two situations, i.e., Tp < Tf (a and b) and Tp > Tf (c and d), where Tp is the resonance period of the estuary and Tf is the tidal forcing period: (a and c) shrinkage associated with a reduction of bay length “l” (type-1 shrinkage) and (b and d) shrinkage of the bay relative to the length of tidal waves due to an increase in the water depth “H” or an increase in the tidal wavelength (type-2 shrinkage). The typical dimension of the Elbe estuary was taken from Winterwerp et al. (2013). Broken and solid double-ended arrows illustrate the tidal amplitudes before and after the shrinkage, respectively. (e) Overview of the two-step tidal weakening taken place in Tokyo Bay during the Holocene. Color shadings indicate predicted maximum tidal elevation, roughly half the spring tidal range, at three representative periods: the present day, 7 ka, and 9 ka. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.) 8
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level rise in such an embayment may cause a reduction of tides through type 2 estuarine shrinkage, whereas land reclamation may cause tidal weakening through type 1 shrinkage. It is to be noted that if the resonance period Tp of the estuary is (moderately) larger than the tidal period Tf, i.e., Tp > Tf, the estuarine shrinkage will act as to increase the tidal amplitude (Fig. 8c and d), an opposite sense compared to the case Tp < Tf which we have verified for the case of Tokyo Bay. Enhancement of semi-diurnal tides due to an increase in the water depth reported in several modern European estuaries (Winterwerp et al., 2013), where Tp is larger than Tf, could be recognized as a tidal enhancement due to the type 2 estuarine shrinkage (Fig. 8d).
Egbert, G.D., Ray, R.D., Bills, B.G., 2004. Numerical modeling of the global semidiurnal tide in the present day and in the last glacial maximum. J. Geophys. Res. 109, 15. https://doi.org/10.1029/2003JC001973. C03003. Endo, K., 2015. “Chuseki–so” in Japan—Latest Layer Bridging the Past and the Future. Fuzanbo International, Tokyo, pp. 416pp (in Japanese). Endo, K., Ishiwata, S., Hori, S., Nakao, Y., 2013. Tokyo Lowland and Chuseki-so: Formation of the soft ground and Jomon Transgression. J. Geogr. 122 (6), 968–991. https://doi.org/10.5026/jgeography.122.968. (in Japanese with English abstract). Endo, K., Kosugi, M., Matsushita, M., Miyachi, N., Hishida, R., Takano, T., 1989. Holocene environmental history in and around the paleo–Nagareyama Bay, central Kanto Plain. Quat. Res. (Daiyonki Kenkyu) 28 (2), 61–77. https://doi.org/10.4116/jaqua.28.61. (in Japanese with English abstract). Endo, T., 2004. Historical review of reclamation works in the Tokyo Bay area. J. 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6. Conclusions Our numerical simulation results indicate that tides in Tokyo Bay during the early to middle Holocene were stronger than those at present and that tidal conditions during these periods in the upper bay were mesotidal, mainly because of the enhancement of semi-diurnal tides, in contrast to the present microtidal setting. The maximum elevation at the bay head was 72% higher at 7 ka than it is at present, whereas tidal currents at the bay mouth were three times stronger during 9–10 ka than under present-day conditions. When tides were compared at a fixed location, tidal amplitudes were largest at 9 ka and decreased over time in two phases: from early to middle Holocene, the weakening was caused by the large rise of sea level (type 2 estuarine shrinkage), whereas from the middle to late Holocene, river delta progradation (type 1 estuarine shrinkage) was responsible for the amplitude decrease. In this study, we have introduced the concept of type 1 and type 2 estuarine shrinkage, associated with the reduction of bay length and with the increase in the water depth, respectively. It was found that estuarine shrinkage may work to weaken tides when the resonance period is shorter than the tidal forcing period (Tp < Tf), as in the case of Tokyo Bay, but it can also enhance tides when Tp > Tf as in the case of the Elbe River Estuary. Though this concept is based on a simple onedimensional resonance theory and has limitations, it may provide a useful measure to assess possible tidal changes in elongated embayments or estuaries. Declarations of interest None. Acknowledgements Authors would like to thank four anonymous reviewers for their valuable comments. This study was supported by JSPS KAKENHI Grant Number JP18K03761. References Akutsu, J., 1973. Geology of the Kawasaki to Kisarazu Subsurface Section, Central Part of Tokyo Bay, Japan, Tohoku University Scientific Report, 2nd series (Geology), Special Volume no. 6 (Hatai Memorial Volume). pp. 465–476. http://hdl.handle.net/10097/ 29004. Arbic, B., Mitrovica, J., MacAyeal, D., Milne, G., 2008. On the factors behind large Labrador Sea tides during the last glacial cycle and the potential implications for Heinrich events. Paleoceanography 23, 14. https://doi.org/10.1029/2007PA001573. PA3211. Bureau of Port and Harbor, 2001. Underground Geological Map of Tokyo Bay, 2nd ed. Tokyo Metropolitan Government, Tokyo, pp. 89 (in Japanese). Chujo, J., 1962. On the paleo–Tokyo River: prospected by the sonic prospecting. Earth Sci. (Chikyu Kagaku) 59, 30–39. https://doi.org/10.15080/agcjchikyukagaku.1962. 59_30. (in Japanese with English abstract). de Haas, T., Pierik, H.J., van der Spek, A.J.F., Cohen, K.M., van Maanen, B., 2018. Holocene evolution of tidal systems in The Netherlands: effects of rivers, coastal boundary conditions, eco-engineering species, inherited relief and human interference. Earth Sci. Rev. 177, 139–163. https://doi.org/10.1016/j.earscirev.2017.10. 006.
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