Coastal-Trapped Waves with Several-Day Period Caused by Wind along the Southeast Coast of Honshu, Japan

Transcription

1 Journal of Oceanography, Vol. 56, pp. 77 to 744, 000 Coastal-Trapped Waves with Several-Day Period Caused by Wind along the Southeast Coast of Honshu, Japan YUJIRO KITADE* and MASAJI MATSUYAMA Department of Ocean Sciences, Tokyo University of Fisheries, Konan, Minato-ku, Tokyo , Japan (Received 5 November 1999; in revised form 16 August 000; accepted 5 August 000) Generation and propagation of several-day period fluctuations along the southeast coast of Honshu, Japan, were investigated by analyzing sea level data and by using a numerical model. The sea level data obtained at twelve stations from Choshi to Omaezaki in fall in 1991, showed energy peaks at the 3 6 day period at the eastern stations in this coast. Time lags of the 3 6 day period fluctuations between station and station indicate westward propagation along the coast. However, the energy level of the 3 6 day period fluctuations suddenly decreased south of the Izu Peninsula. Numerical experiments using a two-layer model were performed to clarify the generation and propagation mechanism of the several-day period fluctuations by periodical wind in fall. The amplitude distributions of observed sea level were qualitatively explained by a coastal-trapped wave (CTW) in the numerical experiment. From the discussions on propagation of a free wave, CTW with the characteristics of a shelf wave generated by the wind along the northeast of the Boso Peninsula was separated into two types of wave at the southeast of the peninsula. One is an internal Kelvin wave with large interface displacement and the other is the shelf wave propagating over the northern part of the Izu Ridge. The sudden decrease in the surface displacement with the 3 6 day period observed at the western stations is considered to be due to the local effect of the wind and phase relation between the internal Kelvin wave and shelf wave. Keywords: Coastal-trapped wave, internal Kelvin wave, shelf wave, several day period, sea level variation, Sagami Bay, two layer model. 1. Introduction Response of coastal water to alongshore wind stress is well known as coastal upwelling or downwelling (Yoshida, 1955), which generally propagates along the coast with flat bottom on its right in the northern hemisphere as an internal Kelvin wave (Gill and Clarke, 1974; Suginohara, 1974). On the other hand, a continental shelf wave is generated by the wind forcing over the continental shelf in a homogeneous ocean (Robinson, 1964; Mysak, 1967; Gill and Schumann, 1974). When both stratification and topography exist, hybrid waves with characteristics of both internal Kelvin and shelf waves called coastal-trapped wave (CTW) are formed along the coast (Gill and Clarke, 1974). Properties of such waves have been clarified by Kajiura (1974), Allen (1975), Clarke (1977), and Huthnance (1978). The wave prop- * Corresponding author. ykitade@tokyo-u-fish.ac.jp Copyright The Oceanographic Society of Japan. erty is roughly determined by the stratification parameter, S = λ /D, where λ is the internal radius of deformation and D is the horizontal scale of shelf (Huthnance, 1978). For S >> 1, the wave has a characteristic of the internal Kelvin wave, and for S << 1, it has a characteristic of the continental shelf wave. Observational results along the east and southeast coast of Honshu, the main island of Japan, indicate existence of both the continental self and the internal Kelvin waves. Kubota et al. (1981) found current and sea level fluctuations with a period of about 100 hours off the coast of Fukushima, about 00 km north of Choshi (Fig. 1). Kubota (1985) indicated that the current fluctuations are closely related to the second mode of a continental shelf wave with zero group velocity, while the sea level fluctuations are due to the first mode of the shelf wave. In addition, he pointed out that the shelf waves are generated by local wind stress. Kusano (1983) also observed a continental shelf wave from moored current measurements off the coast of Ibaraki near north to Choshi. In Sagami Bay, several-day period (hereafter SDP) fluctua- 77

2 Fig. 1. Bottom topography around the southeast coast of Honshu, Japan. Sea level variations were observed at twelve tidal stations. Numerals on the bottom contour line are in meters. Inset at the top of the figure shows location of study area. tions of water temperature and current velocity were frequently observed (e.g. Matsuyama et al., 1980). Recently, Kitade et al. (1998) clarified property and behavior of the SDP fluctuations of current and temperature observed in Sagami Bay, and concluded that the SDP fluctuations are closely related to an internal Kelvin wave caused by local wind through the data analysis. Using an analytical model, they showed that most of the 5 6 day period (SDP5) fluctuations are not generated in Sagami Bay, and are propagated from outside of Sagami Bay. The generation area of the SDP fluctuations in Sagami Bay is speculated as the coast of the Boso Peninsula, but it is still unclear. In addition, the observational results indicated a remarkable difference in the characteristics of CTW with several-day period between in Sagami Bay and off the coast of Fukushima and Ibaraki. Since the SDP fluctuations in current records have high spectral energy level in comparison with predominant semidiurnal internal-tides in Sagami Bay, they are considered to play an important role in water exchange or mass transport around the southeast coast of Honshu. The main purpose of this study is to identify the generation area and clarify the propagation mechanism of the SDP fluctuations along the southeast coast of Honshu by using a numerical model. In addition, we try to explain the difference of characteristic of CTW between Sagami Bay and the eastern coast of Honshu. The SDP fluctuations of sea level and wind in the study area are characterized in Sections and 3, respectively. The numerical model is described in Section 4 and the model result is presented in Section 5. The model result is compared with observational results and the generation and propagation mechanisms of SDP fluctuations in the model are discussed in Section 6. The final section summarizes the results of numerical computation and observations.. Sea Level Fluctuations In order to clarify the properties of the SDP fluctuations, hourly sea level data obtained at twelve tide gauge stations were examined (Fig. 1). The sea level data at Hiratsuka were obtained at the observation tower off Hiratsuka, operated by the National Research Institute for Earth Science and Disaster Prevention. The other sea level data were offered by the Japan Oceanographic Data Center. Barometric data obtained hourly by the Japan Meteorological Agency were used to remove barometric effects from the sea level data. 78 Y. Kitade and M. Matsuyama

3 Fig. 3. Distribution of the spectra energy density, S(ω) cm /cph, for sea level variation from September 1 to November 30, Numerals on the contour line indicate the value of logs(ω). Fig.. Time series of sea level variation. The sea level data were adjusted by removing the barometric effect and by eliminating the tidal components using a tide-killer filter. Figure shows time variations of the sea level adjusted by eliminating diurnal and semidiurnal tidal components by tide-killer filter (Thompson, 1983) after removing the barometric effect under the hydrostatic approximation. The characteristics of the fluctuations were found as follows: (1) the fluctuations with period of 7 days exist at all stations throughout the period, and are more remarkable in September November than in June August; () their amplitudes are the largest at Choshi, the easternmost station, and the smallest at Oshima, an island in Sagami Bay (Fig. 1); (3) remarkable depressions of sea level are found at the end of August and at the end of September; (4) a sea level rise occurred in the middle of October exceeds 10 cm in displacement, and continued for about 10 days; and (5) most of the falls and rises of sea level occur earlier at farther eastern station and earliest at Choshi. Figure 3 shows power spectra of the sea level variations during the period from September 1 to November 30, 1991, during which the SDP fluctuations are remarkable. An energy peak at the period of 5 6 day (SDP5) is significant at the eastern stations from Choshi to Hiratsuka. The high energy level of the SDP5 fluctuation at Choshi, Mera, Tokyo and Yokosuka is nearly equal to each other. On the other hand, there is no energy peak and the energy level is relatively low at the western stations, i.e. Oshima, Minami-Izu, Uchiura, Shimizu and Omaezaki. The energy decrease between Hiratsuka and Minami-Izu is more remarkable at the periods of 3 4 day. In contrast, the energy level difference among the stations is small at 3 day period. Energy of.6-day period at Uchiura located at the head of Suruga Bay is higher than at Aburatsubo and Hiratsuka in Sagami Bay. Spectral peaks of the 3 day period are not found at the eastern stations, except energy peak at.-day period at Tokyo. Table 1 represents coherence and time lag of sea level fluctuations between station and station. The periods of 19, 84 and 6 hours were chosen as a typical period of 5 6 day, 3 4 day and 3 day, respectively. The time lag of high coherence with more than 95% confidence level is underlined. High coherence is found among nearby stations for the three periods except between Hiratsuka and Minami-Izu. The positive time lags of the high correlation suggest westward propagation of the periodic fluctuations along the coast. The fluctuations at Yokosuka lead to those at Tokyo and at Aburatsubo, and time lag of the fluctuations between Choshi and Tokyo for all periods is longer than that between Choshi and Aburatsubo. These results suggest that the most of SDP fluctuations in Sagami Bay were not coming from Tokyo Bay, but directly from Choshi or Mera through the mouth of Tokyo Bay. Thus, the energy peak at.-day period at Tokyo found in Fig. 3 may be the phenomena occurred only in Tokyo Bay. 3. Property of Wind Since the SDP fluctuations of water temperature, current velocity and sea level in Sagami Bay are closely Coastal-Trapped Waves with Several-Day Period Caused by Wind along the Southeast Coast of Honshu, Japan 79

4 Table 1. Time lag (upper), estimated from the phase difference, and coherence (lower). Time lag, whose coherence is greater than 95% confidence level, are denoted by underline. (a) 5 6 day (19-hour) period (b) 3 4 day (84-hour) period 730 Y. Kitade and M. Matsuyama

5 Table 1. (continued). (c) 3 day (6-hour) period correlated with wind fluctuation (Kitade et al., 1998), wind data obtained hourly at Choshi, Oshima and Omaezaki by Automated Meteorological Data Acquisition System (AMeDAS) and at the observation tower off Hiratsuka were analyzed in order to invent the wind model. Figure 4 shows the time variations of the winds during the period from June 1 to November 30, The component of land-sea breeze was already removed by taking 4-h running average. The northward and/or northeastward winds are predominant in early summer, whereas southward and/or southwestward winds are dominant in fall. Especially strong southward winds are found in the middle of October when the significant sea-level rise occurs (see Fig. ). The SDP fluctuations of wind are also found throughout the record. The variation of meridional wind during September November is composed of the constant southward wind and the SDP variations. The SDP wind variations can be considered to be caused by sequential passage of high and low pressures, which move from the southwest to the northeast along the southeast coast of Honshu in fall (Shiraki, 1995). The fluctuation of meridional wind at Oshima leads that at Choshi by about 6.4 hours for 5 6 day period, about.8 hours for 3 4 day period and about 7.3 hours for 3 day period, respectively. In order to examine sea level response to the wind, let us consider a gain factor, G obs, in the single-input linear system (Bendat and Piersol, 1971), namely, G obs S ( ω) ( ω)= α( ω) S ( ω ) where S T and S W are power spectra energy density of sea level and northward component of the wind fluctuations, respectively, α is the coherence between these fluctuations, and ω is the frequency. A large gain factor indicates that the sea level fluctuation is effectively caused by the wind. Figure 5 shows the distribution of the gain factor estimated from the spectra energy density of sea level fluctuation at each tidal station and the spectra energy density of the wind fluctuation at Oshima from September 1 to November 30. The gain factor at all stations is almost the same value for the period longer than 10 days. On the other hand, the gain factors for periods of 3 4 day and 5 6 day suddenly decrease between Hiratsuka and Minami-Izu. This suggests that the sea level fluctuations of these periods are caused by the wind along the coast of the Boso Peninsula and Sagami Bay or propagate there after caused by wind, and that the wind-forced fluctuations are abruptly reduced along the western coast of Sagami Bay. For about.6-day period, the gain factor is the largest at Choshi, and smallest in Sagami Bay. The value at Uchiura and Shimizu in Suruga Bay is slightly larger than that at Aburatsubo and Hiratsuka in Sagami Bay. The distribution of gain factor with each period will be explained by the numerical modeling. T W 1 / Coastal-Trapped Waves with Several-Day Period Caused by Wind along the Southeast Coast of Honshu, Japan 731

6 Fig. 5. Distribution of the gain factor, G obs ( 10 sec.), during the period from September 1 to November 30, shown in the previous section. So, we will investigate the generation and propagation mechanism of coastaltrapped wave by wind along the southeast coast of Honshu in Japan by numerical model to clarify the above observed features. A two-layer model is suitable to express both continental shelf wave and internal Kelvin wave. Under f-plane, hydrostatic and Boussinesq approximations, basic equations for the upper layer are given by Fig. 4. Time series of 4-hour running averaged wind vector. 4. Modeling The SDP fluctuations of current and temperature in Sagami Bay were explained as propagation of the internal Kelvin wave (Kitade et al., 1998). On the other hand, these of the current and sea level at the northeast coast of the Boso Peninsula are mainly induced by the continental shelf waves (Kubota et al., 1981; Kusano, 1983; Kubota, 1985). It is clear that the characteristic of CTW in Sagami Bay is different from that of the northeast coast of the Boso Peninsula. Therefore, these results suggest a coupling between continental shelf wave and internal Kelvin wave in the region of steep depth change of the southeast coast of the Boso Peninsula. In addition, the gain factor for sea level response to the wind is significantly different between Sagami and Suruga Bays, as U1 + ( U1 h ) U1 + f U1 t = gh Ah hu1 s ρ η η η γ a WW γ i u u ρ ( ) + + () 1 η 1 h U1 h U t = ( ) and for the lower layer U + ( U h ) U + f U t ρ1 ρ = gh ( + η) hη1 gh ( + η ) hη + Ah hu ρ ρ i + γ uu γ b UU ( h + η ) 1 () 3 η h 4 t U, = ( ) 73 Y. Kitade and M. Matsuyama

7 Fig. 6. Computational domain. A realistic coastline and simplified bottom topography were used in this study; depths greater than 1000 m and shallower 150 m were set to 1000 m and 150 m, respectively. where h = i / x + j / y, i and j are the unit vectors of x (eastward) and y (northward) axes, respectively, U the volume transport vector, u the velocity vector, and u the difference of velocity vector between the upper and lower layers (u = u 1 + u ), η the vertical displacement of surface (η 1 ) and interface (η ), h the mean layer thickness, W the wind velocity vector, f the vector of Coriolis parameter ( f = s 1 ), t the time, g the gravitational acceleration (9.8 m s ), ρ a the air density, ρ the water density, ρ the density difference between the upper and lower layers, A h the coefficient of horizontal eddy viscosity, γ s, γ i and γ b and are the frictional coefficients at the surface, interface and bottom, respectively. The subscripts 1 and indicate the upper and lower layers, respectively. The coast lines and bottom topographies, 440 km from north to south and 450 km from east to west, were obtained from the chart with km km grid point resolution. For simplicity, the depths shallower than 150 m and deeper than 1000 m were set to 150 m and 1000 m, respectively (Fig. 6). Computational domain was extended to 540 km (from north to south) and 600 km (from east to west) to reduce the influence of the open boundaries. Figure 7 shows phase speed of an internal Kelvin wave for the first vertical mode (solid line) against various water depths. The phase speeds at various depths were estimated from the mean of two density profiles obtained near the center of Sagami Bay by the Kanagawa Fisheries Research Institute on September 3 and October, Dashed line in Fig. 7 indicates the phase speed of Fig. 7. Phase speed of an internal Kelvin wave at various water depths. C 1 means the phase speed for first vertical mode calculated from the mean of two density profiles obtained at the center of Sagami Bay on September 3 and October, 1991 (solid line). The phase speed in the two-layer model is estimated under the stratification condition of h 1 = 130 (m) and ρ/ρ = (dashed line). internal Kelvin wave under the stratification condition of h 1 = 130 (m) and ρ/ρ = Although the upperlayer thickness of 130 m is larger than the thickness of surface mixed layer off the southeast of Honshu in fall, it was determined to express the phase speed of internal Kelvin wave. The phase speeds of internal Kelvin wave in the model almost agrees with that of the first vertical mode of internal Kelvin wave for the observed density profile. The coefficients of surface friction γ s and horizontal eddy viscosity A h were and 50 (m s 1 ) in the model, respectively. The bottom friction coefficient, γ b, and interface friction coefficient, γ i, were assumed as and , respectively, except near the open boundary. These values are usually used on the numerical experiment in the coastal region. In order to suppress the disturbance near the open boundary, clamped (η 1 = η = 0) and sponge condition were applied along the open boundary and in the shadowed area (Fig. 6), respectively. The clamped condition allows surface Ekman transport across the open boundary (Chapman, 1985). The sponge is a region of increasing the frictional coefficients of interface and bottom. The clamped condition was imposed at the outer edge of the sponge. In order to reduce amplitude of the disturbance in Tokyo Bay, sponge condition was also applied to the whole bay. This application may be supported by the time lags of sea level between Tokyo and other stations discussed in Section. Non-slip boundary condition was applied along the coast. The numerical experiment was performed by integrating Eqs. (1) (4) after transforming into finite difference forms, in which the centered difference and the leapfrog scheme were used for spatial and temporal differ- Coastal-Trapped Waves with Several-Day Period Caused by Wind along the Southeast Coast of Honshu, Japan 733

8 Table. The horizontal wave number and frequency of wind distribution for each case. Case 1 (Continuous) Case (6.0-day period) Case 3 (3.5-day period) Case 4 (.6-day period) k, l (m 1 ) ω (s 1 ) ences, respectively. In addition, the Euler-backward scheme was applied every 0 steps to prevent numerical instability. On a basis of the characteristics of sea level, wind, and the gain factor from September through November in 1991, four cases of experiment were assigned to the uniform southward wind (Case 1) and the fluctuations of meridional wind with periods of 6.0-day (Case ), 3.5- day (Case 3) and.6-day (Cases 4). The uniform southward-wind calculation as a preliminary experiment is performed to understand the response of coastal water to the wind (Case 1). The distribution of the wind in Cases, 3, and 4 are approximated by ( ) w = w0 cos kx + ly ω t, where w is the wind speed, w 0 the amplitude of wind speed, and k and l are the zonal and meridional wave numbers for meteorological disturbance, respectively. To reduce the initial disturbance, the wind amplitude was linearly increased with time in a form of w 0 1 7t / t0 ( m s ) for 0 t < t0, = 1 7 ( ) t0 t m s for, where t 0 is the setup time of wind. The t 0 is 0 hours in all cases. Since mean of time lags of the SDP fluctuations of wind between Oshima and Choshi is about 6 hours (Section 3), the propagation speed of the meteorological disturbance is about 30 kilometers par hour, if we suppose it propagates northeastward (45 T). Thus, the wave numbers in the propagation direction of the disturbance can be estimated at m 1 for 6-day period, m 1 for 3.5-day period, and m 1 for.6-day period. The wave number and frequency in each case are represented in Table. 5. Results of the Numerical Experiment 5.1 Maximum displacements of surface and interface Figure 8 shows the distributions of maximum displacements of sea surface and interface in Cases 1 4. As expected from the propagation property of CTW, amplitudes of both surface and interface displacements are greater along the coast or shelf edge than offshore region for all the cases. However, the value along the coast is almost uniform in Case 1, while it is considerably different in Cases, 3 and 4. In Case, the amplitude of surface displacement near the tip of the Izu Peninsula is approximately half of that in both Sagami and Suruga Bays; and in Suruga Bay it is slightly smaller than in Sagami Bay, but, the interface displacement is not different between both bays. In Case 3, the amplitude of surface and interface displacement is obviously smaller near the tip of the Izu Peninsula and in Suruga Bay than the other coastal region. On the other hand, the amplitudes of interface and surface displacements in Suruga Bay are much larger than those in Sagami Bay in Case 4. The amplitude of interface displacement in Cases, 3 and 4 become abruptly large at the southeast of the Boso Peninsula, where the width of continental shelf decreases. Such large interface displacements are considered to be generated due to the spatial change of bottom topography. This will be discussed in the next section. 5. Response of coastal water to the uniform southward wind forcing As shown in Fig. 1, the study area has a very complicated coastal topography. The preliminary experiment was performed to grasp a formation and movement of coastal phenomena such as upwelling and downwelling under the uniform wind condition. This experiment provided useful information to understand the forced motion by the periodic winds. The distribution of interface displacement in Case 1 (Fig. 9(a)) indicated a weak downwelling at the southeast coast of the Boso Peninsula at t = 0 hours, while coastal upwelling is formed near the heads of Sagami and Suruga Bays. At t = 40 hours, the downwelling formed at the south of the Boso Peninsula is strengthen, while the upwelling in both bays is gradually weakened. The interface depression is significant near the south coast of the Boso Peninsula, whereas the surface rise is formed along the eastern coast of the peninsula at the same time (Fig. 9(b)). At t = hours, the surface elevation associated with the interface depression propagates westward along the coast with the speed 734 Y. Kitade and M. Matsuyama

9 Fig. 8. Distributions of the amplitude of surface (left) and interface (right) displacements for each case. of about 1.7 m s 1, which agrees with that of the internal Kelvin wave in this stratification condition (Fig. 7). Therefore, the internal Kelvin wave is considered to be generated near the south coast of the Boso Peninsula and propagate in the Sagami Bay coast with phase speed of 1.7 m s 1. The interface depression and surface rise in relation to the internal Kelvin wave is found to move along the coast toward the west further with time. On the other hand, the mm contour line of surface displacement already reached at western boundary at t = 40 hours. This surface displacement is not associated with the interface displacement, so that it is due to a barotropic motion (hereafter call quasi-barotropic wave). 5.3 Response of coastal water to the periodical wind forcing several day period Figures 10(a) and (b) shows time series of the distributions of interface and surface displacements at every 16-hour interval in Case (6-day period). The large interface depression is found at the southeast coast of the Boso Peninsula for southward wind (t = 7 88 hours). It propagates westward along the coast from Sagami Bay to Suruga Bay, with a characteristics of the internal Kelvin wave, when the northward wind is prevailing (t = hours). The northward wind may induce the upwelling along the eastern side of the Izu Peninsula (Kishi, 1976, 1977) and downwelling along the western Coastal-Trapped Waves with Several-Day Period Caused by Wind along the Southeast Coast of Honshu, Japan 735

10 Fig. 9. Interface (a) and surface (b) displacements in Case 1 from 0 hours to 10 hours. Arrow and numeral at the left of each figure indicate the wind direction and the wind speed (m s 1 ) at the Oshima Island, respectively. side of the peninsula. Therefore, the northward wind may reduce the interface depression from southeast of the Boso Peninsula to the eastern side of the Izu Peninsula, but may reinforce it on the western side of the peninsula. As a result, the interface displacement may be smaller near the tip of the Izu Peninsula than at the head of Sagami and Suruga Bays. On the other hand, the northward wind also causes a surface depression along the eastern coast of the Boso Peninsula. At t = 336 hours, the surface depression expands southwestward all along the southeast coast of Honshu, except close shore. The surface depression with large horizontal scale is expected due to quasi-barotropic wave because it is not associated with interface displacement. Thus, the surface rise associated with downwelling in Suruga Bay may be reduced by the negative surface displacement due to quasi-barotropic wave. The southward wind forms just inverse phenomena in this area. The surface displacement associated with the interface displacement is found along the coast from the southern side of the Boso Peninsula to eastern side of Suruga Bay in Case 3 (3.5-day period) shown in Figs. 11(a) and (b). These displacements are remarkably reduced on the western coasts of Sagami and Suruga Bays. The large interface depression is also formed near the south coast of the Boso Peninsula at t = 180 hours, and propagates along the coast into Sagami Bay with time (Fig. 11(a)). When 736 Y. Kitade and M. Matsuyama

11 Fig. 10. Same as Fig. 9, but in Case from 56 hours to 336 hours. the northward wind becomes gradually strong (t = 190 hours), this interface depression reaches on the western coast of the Sagami Bay head. The northward wind rises up the interface along the western coast of Sagami Bay, so that the interface displacement propagated from the south coast of the Boso Peninsula is reduced with time. When the wind direction turns to southward (t = 0 to 30 hours), this interface depression propagates along the eastern coast of Suruga Bay. The southward wind may rise up the interface along the eastern coast. As a result, the interface depression generated near the south side of the Boso Peninsula may be reduced along the coast of the Izu Peninsula by the local effect of the wind. This process is also applied to the reduction of the interface rise. Two effects strongly contribute to depress surface displacement with this period in Suruga Bay. One is the local effect of the wind, which acts to weaken the displacement along the coast of the Izu Peninsula. The other is that the surface displacement due to the internal mode is out of phase to that due to quasi-barotropic wave. Both effects may act a different role at different area by a given wind period. In the experiment of.6 day period (Case 4), the interface displacement may be amplified along the coast of the Izu Peninsula by the local effect of the wind, and the surface displacement may be amplified by the inphase contribution between the internal Kelvin wave and quasi-barotropic wave in Suruga Bay (Fig. 8). Coastal-Trapped Waves with Several-Day Period Caused by Wind along the Southeast Coast of Honshu, Japan 737

12 Fig. 11. Same as Fig. 9, but in Case 3 from 180 hours to 30 hours. 6. Discussion 6.1 Comparison of observed results and numerical model results The amplitude of surface displacement obtained by the experiments for Cases, 3 and 4 are possible to be compared with observed sea level by a gain factor. A gain factor for the model is defined as G m Ai =, w 0 where A i and w 0 are the amplitudes of the sea surface displacement and of the wind, respectively. We try to compare the numerical model result with observed one by gain factors, G m and G obs. Table 3 presents the gain factors at the tide gauge stations by the observation and at the same stations by the model. The ratios of G obs to G m are in the same order except at Choshi for all three periods and Omaezaki for 6-day period. The amplitude of sea level calculated by the model is roughly one-third of the observed one. Thus, the numerical model results in Cases, 3 and 4 explain qualitatively the observed distributions of sea level along the southeast coast of Honshu, Japan. In addition, the purpose of this study is not only to simulate the amplitude of sea level, but also to clarify the gen- 738 Y. Kitade and M. Matsuyama

13 eration mechanism and propagation process of the SDP fluctuations by using a simple model. In order to compare the numerical results with the observed record, in Fig. 1, we show the time variations of the interface (thick line) and surface (thin line) displacements at each tide gauge station (Fig. 1) and of the wind at Oshima Island in Case. The inertial period (about 1 hours) fluctuations were already filtered out by Fig. 1. Time series of the surface (thin line) and interface (tick line) displacement in Case at the point corresponding to each tide gauge station. Upper panel shows the time series of the wind at Oshima Island. -hour running average. The amplitude of surface displacement at Choshi is almost equal to that at Katsuura and at Mera, while the amplitude of interface displacement at Choshi is much smaller than that at Katsuura and at Mera. In addition, the surface and interface displacements are almost sinusoidal curves at the eastern stations, from Choshi to Hiratsuka, while they are distorted at the western stations and their amplitudes become gradually small. These results can be compared with the observed ones reported by Kitade et al. (1998). The temperature rise, i.e. descent of seasonal thermocline, for the SDP5 fluctuations observed at the head of Sagami Bay lagged behind the northward wind by about 53 hours. The model result shows the descent of interface at the head of Sagami Bay to lag behind the southward wind at Oshima by about 50 hours. Both time lag agrees well with each other. Thus, we may say that the simple model almost represents the SDP5 fluctuation observed in Sagami Bay. Matsuyama et al. (1997) reported the Kyucho in Sagami Bay induced by Typhoon 8818, and described the coastaltrapped wave from analysis of the temperature, current and sea level fluctuations along the bay coast with 7 8 day period. The sea level at Aburatsubo and temperature at 60m depth off there are approximately in phase. This result also agrees well the phase relation between surface and interface displacements shown in Fig Structure of the wave As shown in Fig. 8, the amplitudes of interface displacement in Cases and 3 abruptly increase at the southeast of the Boso Peninsula, where the width of continental shelf changes (Fig. 1). Such increase of the interface displacement is expected for internal waves to be generated due to the spatial change of bottom topography. So, we will investigate the generation mechanism of such phenomenon in detail. The generation is supposed to oc- Table 3. Gain factor ( 10 sec.) obtained by the observation and the model. Coastal-Trapped Waves with Several-Day Period Caused by Wind along the Southeast Coast of Honshu, Japan 739

14 Fig. 13. Amplitude distributions of surface (a) and interface (b) displacements in Case 5. Forcing region is shadowed. Amplitude distributions of surface displacements due to barotropic (c) and baroclinic (d) components in Case 5. cur without wind forcing effect. Hence, it is difficult to identify the detailed mechanism by the result of Cases and 3. The new experiment, which uniform meridional wind forcing with 6-day period is only acted over 00 km from the northern boundary of the computational domain, was performed for free wave to propagate at the southeast of the Boso Peninsula (Case 5). The amplitude along the Boso Peninsula coast obtained in Case 5 (Fig. 13) is about a half of that in Case (Fig. 8) for the limitation of the forcing region northeast of Choshi. The large amplitude of interface displacement is identified to be abruptly generated at the southeast of the Boso Peninsula (Fig. 13). In order to discuss generation mechanism, we divide surface displacement into barotropic and baroclinic modes as follows, η 1i ( ) µ i µ sη η1 = µ µ s i ( ) µ s η 1 µ iη, and η1s =, µ µ s i respectively, where µ s = h/h, µ i = g h /(g h gh), g = g ρ/ρ, η 1i and η 1s are the contribution of baroclinic and barotropic components of the surface displacement, h the water depth, and h the thickness of lower layer (e.g. Gill, 198). Figures 13(c) and (d) show the amplitude distribution of the barotropic and baroclinic components, respectively. The contribution of both components is clearly separated at the southeast of the Boso Peninsula, that is, the barotropic component is dominant along the northeast of the Boso Peninsula, while the baroclinic component is dominant from the southeast of the peninsula to Suruga Bay. The baroclinic component is easily understood to be close relation to the interface displacement. Figures 14(a) and (b) show the distribution of surface displacement due to the baroclinic and barotropic components, respectively. At t = 70 hours, the barotropic component caused along the north coast of Choshi by southward wind reaches at the southeast of the Boso Peninsula, while the baroclinic component is little disturbance there. At t = hours, the barotropic component is amplified at the same region and the baroclinic component is generated at the southeast of the peninsula. At the southeast coast of the Boso Peninsula, the region of contour-line concentration of barotropic component coincides with that of contour-line appearance of the baroclinic component. This indicates a coupling between barotoric and baroclinic modes in this region. At the head of Suruga Bay, the amplitude of baroclinic component is 4 mm (Fig. 13(c)) in spite of that of surface displacement of 3 mm (Fig. 13(b)). This is explained in the following process. The quasi-barotropic 740 Y. Kitade and M. Matsuyama

15 Fig. 14. Sea-surface displacements due to baroclinic (a) and barotropic (b) components in Case 5 from 70 hours to 30 hours. Numerals on the contour line are in millimeters. Arrow and numeral at the top of each figure indicate the wind direction and the wind speed (m s 1 ) at the forced region, respectively. wave is indicated by 1 mm contour line extending from east of the Boso Peninsula to Suruga Bay and propagates westward with speed of about 3.0 m s 1 at t = hours (Fig. 14(b)). On the other hand, the surface displacement of baroclinic component caused by the barotropic component at the southeast of the Boso Peninsula also propagates westward with a speed of 1.7 m s 1 along the coast of Sagami and Suruga Bays at t = hours (Fig. 14(a)). In Suruga Bay, the surface displacement of baroclinic component is out of phase with that of the barotropic component for 6-day period wind forcing. This result suggest that the amplitude variation of surface displacement along the coast is caused by superposition of both the barotropic and baroclinic waves with different phase speeds, i.e. different wave numbers. The wave number increases as increasing frequency in the case for long CTW (e.g. Wang and Mooers, 1976). Thus, amplitude minimum and maximum are formed at the shorter distance along the coast from the generation area as increasing frequency (Fig. 8). As the result, the relation between the surface displacements due to quasibarotropic wave and baroclinic component is out of phase for 6-day period, but is in phase for.6-day period, in Suruga Bay. The numerical model in Case 5 indicates that the quasi-barotropic wave is generated along the northeast coast of the Boso Peninsula, and its energy is divided into two types of wave at the southeast of the peninsula. One is baroclinic wave propagating with the phase speed of 1.7 m s 1 along the southeast coast of Honshu, and the other is the quasi-barotropic wave propagating with that of 3.0 m s 1 over shallow region in the north of the Izu Ridge. Coastal-Trapped Waves with Several-Day Period Caused by Wind along the Southeast Coast of Honshu, Japan 741

16 6.3 Characteristics of the wave Considering the characteristics of the wave in the model, it is useful to discuss free wave properties over the continental shelf with width L in a two-layer ocean. A step-like continental shelf was considered for simplicity. From inviscid and linear equations of motion without forcing, and continuity equation, the non approximation form of characteristic equation of the CTW in the two-layer ocean with step-like shelf (Kajiura, 1974) is ( ) ( 1 X1 )( X1 T1) T D D X ( ) r ( 1 X )( X T) 1 r T X ( 1 1 ) r µ r X ( X T) 1 r T1( X1 1) 1 µ r ( 1 r) ( X )( X1 T1) 0, 5 = ( ) where X K i i and ck p f f i D ρ ρ1, Ti tanh KiL, r, µ, D ρ = = ( ) = = = ω c i + c gd ω c, 1 =, p ( ) c g D = D D µ, D where the subscripts 1 and are used to denote the quantities related to barotropic and baroclinic motions, respectively, c p and ω the phase speed and the frequency of CTW, respectively, and D and D* are the water depth and thickness of the lower layer, respectively. Dash denotes the quantity in deeper water. Four roots are obtained by solving the characteristic equation (5) numerically. Figure 15(a) shows the variation of phase speed of CTW with 6-day period versus shelf width L. Phase speed of the waves propagating from southeast of the Boso Peninsula to Sagami Bay in the model is about 1.7 m s 1. Since phase speed of internal gravity wave with non-rotation in shallow region, c, is 0.69 m s 1, c p /c.5. Thus, the wave propagating along the coast of Sagami Bay is considered to be the second mode. According to Kajiura (1974), the characteristic of second mode changes dramatically with the shelf width. At the narrow shelf area, Fig. 15. (a) Phase velocity c p /c as a function of the shelf width fl/c in the two-layer model with step-like shelf where water depths are 150 m in shallower region and 1000 m in deeper region. Each curve was obtained from the characteristic equation (5) for the stratification conditions used in this study. The indexes indicate; dkw; internal Kelvintype wave, SW1; shelf wave, skw1; barotropic Kelvin-type wave in shallow water. The characteristic of the wave is considered to change from SW1 (L = 30 km) to dkw (L = 5 km) at the southeast of the Boso Peninsula. (b) Crossshelf distribution of surface and interface displacement. Left; shelf width L = 5 km, right; shelf width L = 30 km. Dashed line indicates shelf break. where shelf width is narrower than internal radius of deformation ( fl/c (=S 1/ ) < 1), the second mode wave has a characteristic of internal Kelvin wave in the deeper water. As the shelf width increases, the characteristic of a shelf wave appears at the range of 1 < fl/c < 100, and finally it becomes barotropic Kelvin wave in the shallow water region at the range of 100 < fl/c. Figure 15(b) shows surface and interface displacements due to the second mode. Sign of surface 74 Y. Kitade and M. Matsuyama

17 displacement changes around shelf break in both narrow and wide shelf regions. Interface displacement at narrow shelf region (L = 5 km) is the largest at the coast and decreases gradually in the offshore direction. To the contrary, interface displacement at wide shelf region (L = 30 km) is the largest at the shelf break. In Cases and 5 (Figs. 8 and 13(b)), the maximum interface displacement occurs along the shelf edge of east of the Boso Peninsula, while it occurs along the southeast coast of the peninsula and the coast of Sagami Bay. The distributions of surface and interface displacement qualitatively agree well with the wave shapes in the model, although these characteristics have been derived for the motion on the step-like continental shelf, which is uniform in the alongshore direction. This result supports the previous observational results, i.e. the continental shelf wave with several day period is observed at the northeast of the Boso Peninsula while the internal Kelvin wave is observed in Sagami Bay. Thus, the change of main contribution from barotropic mode to baroclinic mode at the southeast of the Boso Peninsula (Fig. 14) is considered to be due to variation of the wave characteristic. Furthermore, the quasi-barotropic wave propagating over the northern part of the Izu Ridge is also considered to be second mode, since its phase speed is about 3.0 m s 1, c p /c 4.3. From the phase speed and wave characteristic, this wave may have a characteristic of shelf wave (Fig. 15(a)). From these discussions, coastal-trapped waves, propagating along the coast, are mainly explained by term of the continental shelf wave at the northeast of the Boso Peninsula, and of internal Kelvin wave in deep water at the south of the peninsula. The wave energy is changed mostly from the shelf wave to an internal Kelvin-type wave at the southeast of the Boso Peninsula and the rest of its energy may propagate as shelf wave, regarding the northern part of the Izu Ridge as shelf and shelf slope. 7. Summary The generation and propagation of several-day period fluctuations along the southeast coast of Honshu in Japan have investigated by analyzing sea level data and by using a numerical model. The sea level data, obtained at twelve tide gauge stations in 1991, showed remarkable energy peaks at the 5 6 day period at the eastern stations, from Choshi to Hiratsuka, and at the 3 day period in Suruga Bay and Tokyo Bay. Time lags of the 3 6 day period fluctuations between stations suggested that the fluctuations propagated from east to west along the southeast coast of Honshu. However, the energy level of the 3 6 day period fluctuations decreased by up to one order in magnitude at the western stations. A numerical experiment using a two-layer model has performed to clarify the generation mechanism of the several-day period fluctuations. Periodical wind, propagating northeastward, was assumed in the two-layer model to express wind distributions in fall. The distribution of sea level fluctuations observed along the southeast coast of Honshu was qualitatively represented by coastaltrapped wave (CTW) in the numerical experiment. The numerical experiment shows that CTW are generated mainly as a shelf wave along the northeast coast of the Boso Peninsula by the periodic wind forcing. From the discussions on propagation of a free wave, CTW with the characteristics of a shelf wave along the northeast of the Boso Peninsula was separated into two types of wave at the southeast of the peninsula. One is an internal Kelvintype wave with large interface displacement, propagating westward along the coast of Sagami and Suruga Bays. The other is the shelf wave, propagating westward over the northern part of the Izu Ridge. The numerical experiments also demonstrate that there are two effects for amplitude modifications in surface displacement of the 3 6 day period fluctuations at the western stations. One is the local effect of the wind, which acts to weaken the displacement along the coast of the Izu Peninsula, and the other is out of phase contribution between surface displacements due to internal Kelvin type wave and quasi-barotropic wave, having a characteristics of the shelf wave. These effects appear at different areas by various periods. In the case of.6 day period (Case 4), interface displacement may be amplified by the local effect of the wind and surface displacement may be more amplified by the in-phase contribution of the barotropic and baroclinic components in Suruga Bay. These results agree well the observational results obtained by the sea level analysis. Acknowledgements We wish to thank Dr. Kinjiro Kajiura for his thoughtful comment, Dr. Chris Garrett and Dr. Kate Stansfield of the University of Victoria for their useful comments and discussions, and anonymous reviewers for their useful comments on the original manuscript. The sea level data at Hiratsuka were obtained at the observation tower off Hiratsuka, operated by the National Research Institute for Earth Science and Disaster Prevention. The other sea level data were offered by the Japan Oceanographic Data Center (JODC). Barometric data and AMeDAS data were offered from the Japan Meteorological Agency. Numerical experiments were performed on the CONVEX computer system at Tokyo University of Fisheries. References Allen, J. S. (1975): Coastal trapped wave in a stratified ocean. J. Phys. Oceanogr., 5, Bendat, J. S. and A. G. Piersol (1971): RANDOM DATA: Analysis and Measurement Procedures. John Wiley & Sons, Inc., New York, 407 pp. Coastal-Trapped Waves with Several-Day Period Caused by Wind along the Southeast Coast of Honshu, Japan 743

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