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Sea-level variations with a several-day period along the southwestern Japan sea coast
ContinentalShelfResearch,Vol. 11, No. 2, pp. 167-182,1991.
0278-4343/91 $3.00+ 0.00 © 1991PergamonPressplc
Printedin Great Britain.
Sea-level variations with a several-day period along the southwestern Japan Sea coast YUTAKA ISODA,* TETSUO YANAGI* a n d HEUNG-JAE L I E t
(Received 29 May 1990; accepted 10 August 1990) Abstract--Daily mean sea-level data obtained along the southwestern Japan Sea coast (the San'In coast of Japan and the east coast of Korea) are analysed using a spectral analysis technique. It is found that a prominent peak period of sea-level variations exists at 3-5 days from January to April. These sea-level variations disappear from May to August. The remaining season, from September to December, has a broad peak at a period of 3-10 days. These sea-level variations are highly coherent with the wind variations. The wind-induced sea-level variations in the frequency band from a 2.5- to 6-day period propagate with the coast to the right-hand side and were non-dispersive. The progressive waves along the San'In coast and the east coast of Korea propagate independently. The wave along the San'In coast can be explained by a first mode shelf wave and begins to propagate from the Tsushima Straits. We cannot specify the type of wave along the east coast of Korea, since it propagates at a speed intermediate between that of a shelf wave and an external Kelvin wave.
INTRODUCTION
IT has been known that persistent low-frequency variability in sea level with a period of several days exists along the southwestern Japan Sea coast, which consists of the San'In coast, the Tsushima Straits and the east coast of Korea (Fig. 1). SHOJI(1961) first pointed out the phenomena that sea-level crests and troughs propagate slowly from south to north along the Japan coast. He also suggested that the wave might be induced by a meteorological disturbance. The propagation characteristics of sea-level changes have been studied using spectral analysis by several investigators (ENDo, 1968; ISOZAKI, 1969; LEE and CmJNG, 1982; LIE, 1984). Their investigation areas are separated into two parts, i.e. along the Japan coast and the east coast of Korea. Table 1 is a summary of evidence for the existence of the progressive wave along the southwestern Japan Sea coast. From these reports, it is clear that sea-level variations with significant spectral peaks propagate with the coast to the right-hand side at speeds of several m s- 1, slower than that of meteorological disturbance (several tens of m s-l). However, the prominent peak periods and propagation speeds proposed by the previous studies are different, even in the same coastal area. The difference may be due to the different period of each investigation as shown in Table 1.
*Department of Ocean Engineering, Ehime University, Bunkyo 3, Matsuyama 790, Japan. tKorea Ocean Research and Development Institute, Ansan, P.O. Box 29, Seoul, Korea. 167
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Here we focus our attention on the periodicity of several days in the whole southwestern Japan Sea coastal area for a 3-year period. Objectives of the present investigation are to elucidate the following areas: (1) How important are the seasonal variations of sea-level change in each coastal area? (2) What is the relationship between the sea-level variations and the meteorological disturbances? (3) What are the typical characteristics of progressive waves along each coast? In particular, it is of interest to delineate whether such waves propagate from the Korean coast to the Japan coast or not. DATA PROCESSING The locations of tidal-gauge stations in this analysis are shown in Fig. I. Tidal data, observed at the east coast of Korea at Sogcho, Mukho and Pohang, were obtained by the Hydrographic Office of Korea. For the Japan coast, Shimonoseki, Hamada, Sakai, Saigo and Maizuru data were obtained from the Japan Oceanographical Data Center (JODC). Hourly data observed during the 3-year period from 1 January 1980 to 31 December 1982 are used in order to investigate the sea-level disturbances with a period of several days. Astronomical tides and inertial oscillations contained in the observed data were filtered out by a tide killer filter (HANAWAand MITSUDERA, 1985) and then daily mean sea levels were obtained. Hourly atmospheric pressure observations taken at weather stations (operated by the Central Meteorology Office of Korea and Japan Meteorological Agency) in the vicinity of tide-gauge stations were used. Daily mean sea-level data were adjusted by the daily mean atmospheric pressure according to the hydrostatic hypothesis ( - 1 c m m b - t). It is considered that the deformation of wind speed and direction at each meteorological station are largely influenced by the local geographical condition of the observatory. On
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the other hand, YANAGI et al. (1984) showed that a uniform (spatially and temporally) wind was blowing above the southwestern Japan Sea with a several hundred km spatial scale. Therefore, the sea surface wind over the study area is assumed to be-the geostrophic wind, w fv y-
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where w (v~, vy) (m s - i ) is the hindcasted geostrophic velocity component; AP (mb) is the atmospheric pressure difference between two stations; AS (km) is the distance between two stations; Pa (=1.0 kg m -t) is the air density; f (=8.5 × 10 -s s -1) is the Coriolis parameter at 36°N. That is, the daily mean northward wind component was calculated from equation (1) using the atmospheric pressure difference between Pohang and Saigo, situated at the same latitude about 36°N with the distance ASx of 420 kin. The daily mean eastward wind component was estimated from the pressure data at Shimonoseki and the mean atmospheric pressure between Pohang and Saigo, and ASy = 280 km. In the present investigation, the above adjusted daily mean sea level, daily mean atmospheric pressure and hindcasted daily mean geostrophic wind are used as the basic data, and hereafter these data are referred to without "adjusted daily mean" or "daily mean".
RESULTS Seasonal characteristics o f sea-level variations
Figure 2 shows the time series of sea level at eight stations along the southwestern Japan Sea coast and of atmospheric pressure at two stations, Sogcho (northern end) and Maizuru (eastern end). The atmospheric pressure variations of these two stations have similar patterns and amplitudes with the period at several days, although the distance between both stations is about 800 km. On the other hand, it can be seen that sea-level variations at stations along the San'In coast differ from those along the east coast of Korea. The sealevel variations along the San'In coast from Hamada to Maizuru show much larger day-today variations when compared with those along the east coast of Korea. Although Shimonoseki in the Tsushima Straits is on the Japan coast side, its day-to-day variations are small and similar to those at stations on the east coast of Korea. However, the seasonal variations of sea level at Shimonoseki are very similar to those at stations along the San'In coast. Figure 3 shows the spectrum of sea level at Mukho, Shimonoseki and Sakai which represent the east coast of Korea, the Tsushima Straits and the San'In coast, respectively. The dynamic spectrum is the analytical method which expresses the dominant periods in terms of isopleths of the spectral density with time. Its detailed analytical method is as follows: (1) Sixty-four (=26) consecutive data (about 2 months) are the basic time series, comprising one group in order to calculate the power spectrum (FFT method). The next
Sea-levelvariations
171
time series delays its beginning day for 20 days from the former one. Thus, we have the 52 groups of the time series during the 3 years from 1980 to 1982. (2) A least squares linear trend is subtracted from each time series to remove the effect of low-frequency variations. (3) The power spectrum (FFT) of each series is calculated in turn. This spectral analysis, i.e. the dynamic spectrum, can represent sea-level variations from a 2- to 32-day period. Hence, Nyquist frequency is 0.5 cpd, the resolution frequency is AF = 0.0156 cpd and the degree of freedom is 4 in each spectral analysis. (4) In drawing the above dynamic spectrum the unit of spectral density is the squared amplitude of the phenomena in order to emphasize the variations with a several-day period. The interval of isospectral density is changed for each station in order to represent the peak periods of sea-level variations. It is seen that the spectral density at Shimonoseki does not peak at periods less than 10 days throughout the year and its density is lower than that of other stations (Fig. 3). The spectral density at both Mukho and Sakai presents similar seasonal patterns about peak periods. That is, their spectral density with 3- to 5-day periods is the highest from January 10 cm(mb) (A.P.}
Sogcho Maizuru (S.L.) SOgcho Mukho Pohang
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to April in 1980 and 1981. In 1982, the high spectral density at Sakai in this season exists at high frequency, i.e. around a 5-day period, and it is not clear at Mukho. On the other hand, this spectral peak disappears from May to August when the variability is at a minimum. From September to December, a broad peak exists at a 3- to 10-day period. Relationship between sea level and meteorological disturbances ISOZAKI (1969) and ENDo (1968) suggested that sea-level variations along the Japan coast with a period of several days were caused by meteorological disturbance with the same period. The relationship between sea level and meteorological disturbances, i.e. atmospheric pressure or wind variations, are investigated using the dynamic spectrum analysis. Figure 4 shows the dynamic spectrum of atmospheric pressure at Shimonoseki and coherence-squared variations between sea levels shown in Fig. 3 and atmospheric pressure at Shimonoseki. Here, as the atmospheric pressure variation at each station along the southwestern Japan Sea coast has very similar properties, those variations are represented
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by that of Shimonoseki. As a measure of statistical significance, 95 and 90% confidence limits of coherence-squared values are 0.78 and 0.68, respectively. The dynamic spectrum of atmospheric pressure shows that no significant spectral peaks exist from May to August, while there are spectral peaks with a period of several days present in the other seasons. Such a seasonal pattern is similar to that of sea level at Mukho and Sakai shown in Fig. 3. Therefore, sea-level variations may be affected by meteorological disturbances. However, the coherence-squared value is low at each station. This result implies that the phase of atmospheric pressure variations is not fixed to that of sea-level variation and it is suggested that sea-level variations cannot be generated effectively by atmospheric pressure variations. Although wind variations have the same periodicity as the atmospheric pressure variations, the phase of wind variations is not necessarily equivalent to that of atmospheric pressure variations. This is because each cyclone and anticyclone take different courses above the Japan Sea. Figure 5 shows the dynamic spectrum of each wind component and the coherence-squared variations among various pairs of seaqevel and wind components. The northward wind component, i.e. the component along the Korean coast, spectrum has a peak at a period of more than 20 days in winter. It is suggested that this low-frequency variation may be concerned with the winter monsoon from the Asian Continent. The variations of eastward wind component, i.e. the component along the San'In coast, occur at periods of 10 days or less. These high-frequency wind variations are very similar to the seasonal pattern of sea-level variations at Mukho and Sakai given in Fig. 3. This relationship is the same as the relationship to atmospheric pressure. However. a significant coherence with a prominent peak period appears in the case of the relationship between wind and sea level. At Mukho, the high coherence distributions of both wind components are very similar to each other. Sea-level variations at Shimonoseki have apparently high correlations with the northward wind component, and those at Sakai have high correlations with the eastward wind component. We suggest that the seaqevei variations along the southwestern Japan Sea coast can be interpreted fairly well, as a wind-generated phenomenon, although sea-level response to wind direction differs at each coastal area. Figure 6 shows the phase variations of wind vs sea level with the coherence-squared value higher than 0.4 at each station. Considering an infinitely long coast, sea level will respond mainly to the Ekman transport induced by the alongshore wind component. The wind component which induces the rise of sea level due to the onshore Ekman transport at each coast is positive. Therefore, a positive phase angle shown in Fig. 6 denotes a lead of wind variation. The phase angle for Mukho suggests that sea level has a different response to each wind component although there are similar coherence variations to both wind components. The phase variations around 90° are dominant for the eastward wind component and 0° to 45° phase angles are dominant for the northward wind component at Mukho. The phase angle with ~ gh correlation for both Shimonoseki and Sakai shows the range of 0° to 45° is dominant. These results imply that the wave may be generated only by the alongshore (eastward) wind component and propagated along the San'In coast. However, we cannot conclude whether the sea-level variations along the east coast of Korea are generated by the offshore (eastward) or alongshore (northward) wind component variations. The sea-level variations at Shimonoseki are related to the offshore (northward) wind component variations. In other words, its relationship is similar to those of Mukho in the east coast of Korea although Shimonoseki faces the Tsushima Straits. Such relations between sea level
Sea-level variations
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Propagation characteristics of sea-level variations Phase speeds were calculated from phase lags for coherence-squared values of more than 0.5. We made the cross-correlation analysis at the following four coastal regions due
176
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'to the difference in bottom topography: (1) the east coast of Korea (Sogcho to Pohang), (2) from the Korean coast to the Japan coast (Pohang to Hamada), (3) along the western (Hamada to Sakai) and (4) eastern region (Sakai to Maizuru) of the San'In coast. The San'In coast was divided into two small regions due to the difference in shelf topography; the shelf width at the western region is wider than that at the eastern region (Fig. 1). The cross-correlation analysis period is classified into three periods, January to April, May to PHASE
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177
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August and September to December, because the prominent peak periods of sea level depend upon the period as shown in the previous section. The estimated propagation speeds for each pair of stations are summarized in Fig. 7. The propagation characteristics of the four regions are as follows: the frequency band with wave propagation characteristics is a 2.5- to 6-day period and there is no remarkable difference in propagation speeds due to the difference in the prominent peak period and the cross-correlation analysis seasons. The former characteristic suggests that the generated waves are non-dispersive. The latter suggests that such waves may be little affected by the seasonal change of the stratification. The phase of sea-level variations along the east coast of Korea propagates southward at a speed of 20-90 m s- 1. The phase of sea-level variations along the San'In coast propagates slower than that of the Korean coast. The sea-level variations in the western and eastern regions of the San'In coast propagate eastward at a speed of about 14 and 5 m s -1, respectively. It is found that these propagation speeds are positive in each coastal area,
178
Y. 1SODAet al.
'that is, this propagation characteristic is consistent with that of the theoretical continental shelf wave or Kelvin wave, which always propagates with the coast on the right-hand side in the northern hemisphere. On the other hand, the propagation speed between the Korean coast and the Japan coast seems to be about 6 m s - ~from Hamada to Pohang, i.e. with the shallow area to the left-hand side. The direction of such phase propagation cannot be explained by the propagation of a shelf or Kelvin wave. Therefore, this observed wave propagation between the Korean coast and the Japan coast may be apparent due to the different propagation characteristics at each coastal area or the topographic effect of the Tsushima Straits. From the results of sea-level analysis, the existence of waves which propagate continuously between the Japan and Korean coastal area is not found. To investigate the type of prominent wave at each coastal area, the theoretical propagation speeds of free waves, i.e. the external Kelvin wave (a), the internal Kelvin wave (b) and the shelf wave (c), are calculated. (a) The external Rossby radius deformation over the shelf is about 2 = \,~,,h(f = 450 kin, where g = 9.8 m s-2 is the gravitional acceleration, h = 150 m the mean depth over the shelf and f = 8.5 x 10 -5 s -1 the Coriolis parameter. Since this radius deformation 2 is several times as large as the shelf width, the depth off the shelf edge (about H = 2000 m) is related to the propagation speed of the external Kelvin wave. Then, its propagation speed is about Ce = V~gH = 140 m s -~. (b) The permanent pycnocline always exists at about 150 m depth between the Japan Proper Cold Water and the Tsushima Warm Water. Therefore, the internal Kelvin wave is possibly trapped at the shelf edge where the pycnocline intersects the shelf slope. Its propagation speed is calculated by Ci = X/~g&ph h ' / H = 1.6 m s -1 , where h(= 1850 m) and h'(=150 m) are the thickness of the lower and upper layers, respectively, Ap (=2 x 10 -3) is the difference in density between both layers and H(=2000 m) is the total depth. (c) Since the coast is an important factor for the wind-induced shelf wave to supply the water column with the vorticity, this type of wave may be trapped by the bottom slope near the coast, The properties of coastal trapped waves when the pycnocline intersects a sloping bottom were studied by KAW~,BF~(1982) using a two-layer model. He denoted that the properties of the upper (lower) shelf wave were almost unaffected by the existence of a lower (upper)-layer slope. Therefore, the barotropic shelf wave trapped by the upper bottom slope is considered. The bottom topography profiles shallower than about 1000 m depth off the coastal areas A, B and C shown in Fig. 1. are approximated by the exponential function as shown in Fig. 8a. The actual bottom topography is represented by a solid line and the model topography by a dotted line. Using the linear theory of barotropic shelf wave with the exponential depth (BuCHWALDand ADAMS,1968), the obtained dispersion relations for the lowest three modes are shown in Fig. 8b. As the observed wave in a forced region is modulated by the wind-forced wave, it cannot represent the true propagation speed of the free wave. For example, two waves with the same frequency, w, unit amplitude and different wavenumbers, kl, k2, are considered. One is the wind-induced free wave (kl) and the other is the wind-forced wave (k2) with the same scale of meteorological disturbances. This problem was treated by GILL and SCHUMANN (1974). They have shown that the amplitude of each wave satisfies a simple, first-order wave equation. That is, the observed (kob: wavenumber) wave has the relationship
Sea-level variations
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180
Y. ISODAel al.
sin (kob x-wt) = sin (klx-wt) + sin (kex-wt) = 2cos ((kl - k~)xl2) sin ((kl + k2)xt2 - wt)).
(2)
Therefore, the observed wave propagation speed Cob is Cob = w/kob = 2w/(kl + k2).
(3)
If the spatial scale of the wind is much larger than that of the free wave, i.e. k2 = 0, Cob = 2w/k~ = 2C,
(4)
where C ( = w / k l ) is the propagation speed of the free wave. On the other hand, if the spatial scale of the wind is the same as that of the free wave, i.e. kl = ke, and the resonance between both waves has occurred, Cob = w/kl = C.
(5)
Equations (4) and (5) show that for equal amplitude of the directly forced and free wave the observed wave propagation speed has a value from one to two times that of the free wave. Thus, when we infer the existence of waves in a forced region from the observed phase propagation speed, we must pay attention to the above wave property. The internal Kelvin w.ave in this study area has a theoretical propagation speed from 1.6 to 3.2 m s -1. However, such slow wave propagation is not observed at every coastal area. We suggest that the sea-level variations only along the San'In coast are first mode shelf waves as shown in Fig. 8. The sea-level variations along the Korean coast cannot be so easily interpreted. The propagation speed of the free wave suggested from the observations is 10-90 m s-1, which is the intermediate speed between the theoretical continental shelf wave (a first mode wave has about 1.5 m s - t phase velocity in the non-dispersive region) and an external Kelvin wave (about 140 m s-t). Sea-level variations in the Korean coastal area have a complicated response to wind due to the existence of unspecified waves and the high correlation in each wind component. DISCUSSION AND CONCLUSION Sea-level data obtained along the southwestern Japan Sea coast from 1 January 1980 to 31 December 1982 have been analysed using the method of dynamic spectral analysis. The results indicate that the seasonal variations of sea level can be roughly divided into three seasons. One has its prominent peak period at 3-5 days from January to April. In the second season significant sea-level variations disappear from May to August. The season from September to December has a broad peak at 3-10 days. These variations of sea level are highly coherent with the hindcasted geostrophic wind variations, while incoherent with the atmospheric pressure variations. This implies that the sea-level variations in the southwestern Japan Sea coast are caused by the prominent peak period of wind variations with the period of several days. The wind-induced sea-level variations in the frequency band from 2.5 to 6 days propagate non-dispersively. However, the progressive waves along the San'In coast and Korean coast exist independently. The existence of waves which propagate continuously between each coastal area cannot be found from this sea-level analysis. By comparing the theoretical wave phase speeds with the observed propagation speeds, we conclude that a first mode shelf wave exists along the San'In coast. This shelf wave is generated by the east-
Sea-level variations
181
west wind variations, i.e. the alongshore wind c o m p o n e n t , and begins to propagate from the exit of the Tsushima Straits situated at the westorn end of the San'In coast. This is because sea-level variations at Shimonoseki facing the Tsushima Straits have relatively lower amplitude and high correlation with the n o r t h - s o u t h wind variation. Although sealevel variations along the Korean coast have a tendency to p r o p a g a t e from north to south, the wave type cannot be specified from its propagation speed. T h e observed propagation speed is intermediate between the theoretical shelf wave and the external Kelvin wave. Moreover, such sea-level variations have a complicated response to wind due to high correlation with both the alongshore and offshore wind component. The results of this study differ from those of LEE and CHUNG (1982) and LIE (1984), especially regarding the observed propagation speed. One possible reason for this m a y be that since the shelf topography along the east coast of K o r e a is relatively steep (Fig. 1), the phase speed of an expected free shelf wave will be very slow, i.e. less than 1.5 m s -1 (Fig. 8). If such a wave exists along the K o r e a n coast, the propagation time from Sogcho to the Tsushima Straits, about 400 km, is m o r e than 3 days. Therefore, it is possible that a shelf wave generated from the f o r m e r meteorological disturbance remains along the Korean coast when a new shelf wave is generated. In the above case, sea-level variations along the Korean coast will b e c o m e very complicated due to mixing between forced and free waves. In this case, a wave-generated area is an important factor, which we cannot detect in this study. W e plan to investigate the wave-generated area and propagation of shelf waves using data f r o m several m o r e close stations along the K o r e a n coast in the near future. Although sea level along the soutwestern J a p a n Sea coast has the variations as described above, the current variations over the shelf m a y not necessarily oorrespond to such sealevel variations at the coast. In fitting the phase speeds of barotropic shelf waves to the data at Taisha Bay in the San'In coast, YANAGI et al. (1984) found that the second m o d e of shelf waves was as dominant as current variations. Such higher m o d e dominance of the current has also been denoted off the Fukushima coast by KOBOTA et al. (1981), off the Oregon coast by HSIEH (1982) and off the east coast of Australia by CHURCH et al. (1986) and FREELAND et al. (1986). These studies denote that the spatial and temporal flow distributions over the shelf due to the wind-induced shelf wave cannot be sufficiently predicted only by the information of sea-level variations at the coast. We will study the characteristics of shelf waves along the southwestern J a p a n Sea coast with the use of sea level and current data in the near future. Acknowledgements--The authors express their sincere thanks to Dr H. Takeoka and Mr H. Akiyama of Ehime University for their helpful discussion and Mr O. Miura for his assistance in data analysis. The data processing was carried out on a FACOM M-360 AP of the Computer Center of Ehime University.
REFERENCES BUCHWALDV. T. and J. K. ADAMS(1968) The propagation of continental shelf wave. Proceedingsof the Royal Society, A365, 235-250. CHURCHJ. A., J. F. HOWARD,H. J. FREELANDand R. L. SMITH(1986) Coastal-trapped waves on the East Australian continental shelf. Part 1, Propagation of modes. Journal of Physical Oceanography, 16, 19291943. ENDOH. (1968) Spectral analysis of daily sea level records along the coast of Japan. Report of Hydrographic Researches, 4, 5-19.
182
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FREELAND H. J., F. M. BOLAND,J. A. CHURCH, A. J. CLARKE. A. M, G. FORBES,A. HUYER,R. L. SMITH, R. O. R. Y. THOMPSONand N. J. WHITE (1986) The Australian coast experiment. A search for coastal-trapped waves. Journal of Physical Oceanography, 16, 1230-1249. GILL A. E. and H. Schumann (1974) The generation of long shelf waves by the wind. Journal of Physical Oceanography, 4, 83-90. HANAWA K. and H. MITSUDERA (1985) O n the data processings of daily m e a n values of oceanographical data. Note on the daily m e a n sea-level data. Bulletin of Coastal Oceanography, 23, 79-87. HSIEH W. W. (1982) Observations of continental shelf waves off Oregon and Washington. Journal of Physical Oceanography, 12, 887-896. ISOZAKII. (1969) A n investigation on the variations of sea level due to meteorological disturbances on the coast of Japan islands (3), O n the variation of daily m e a n sea level. Journal of the Oceanographical Society ofJapan, 25, 91-102. KAWABE M. (1982) Coastal trapped waves in a two-layer ocean: Wave properties when the density interface intersects a sloping bottom. Journal of the Oceanographical Society of Japan, 38, 115-124. KUBOTA M.. K. NAKATA and Y. NAKAMURA(1981) Continental shelf wave off the Fukushima coast, Part 1, Observation. Journal of the Oceanographical Society of Japan, 37, 267-278. LEE J. H. and Y. CHUNG (1982) Continental shelf waves off the eastern coast of Korea. La Mer, 20, 169-180. LIE H. J. (1984) Coastal current and its variation along the east coast of Korea. In: Ocean hydrodynamics of the Japan and East China Sea, T. TCHIYE, editor, Elsevier, A m s t e r d a m , pp. 399-408. SHOJI D. (1961) O n the variation of the daily m e a n sea levels along the Japan islands. Journal Of the Oceanographical Society of Japan, 17, 21-32. YANAGI T., Y. ISODA and N. KODAMA(1984) The long period waves on the San'In coast (in Japanese). Bulletin of the Disaster Prevention Institute, Kyoto University, 27, 611-620.
0278-4343/91 $3.00+ 0.00 © 1991PergamonPressplc
Printedin Great Britain.
Sea-level variations with a several-day period along the southwestern Japan Sea coast YUTAKA ISODA,* TETSUO YANAGI* a n d HEUNG-JAE L I E t
(Received 29 May 1990; accepted 10 August 1990) Abstract--Daily mean sea-level data obtained along the southwestern Japan Sea coast (the San'In coast of Japan and the east coast of Korea) are analysed using a spectral analysis technique. It is found that a prominent peak period of sea-level variations exists at 3-5 days from January to April. These sea-level variations disappear from May to August. The remaining season, from September to December, has a broad peak at a period of 3-10 days. These sea-level variations are highly coherent with the wind variations. The wind-induced sea-level variations in the frequency band from a 2.5- to 6-day period propagate with the coast to the right-hand side and were non-dispersive. The progressive waves along the San'In coast and the east coast of Korea propagate independently. The wave along the San'In coast can be explained by a first mode shelf wave and begins to propagate from the Tsushima Straits. We cannot specify the type of wave along the east coast of Korea, since it propagates at a speed intermediate between that of a shelf wave and an external Kelvin wave.
INTRODUCTION
IT has been known that persistent low-frequency variability in sea level with a period of several days exists along the southwestern Japan Sea coast, which consists of the San'In coast, the Tsushima Straits and the east coast of Korea (Fig. 1). SHOJI(1961) first pointed out the phenomena that sea-level crests and troughs propagate slowly from south to north along the Japan coast. He also suggested that the wave might be induced by a meteorological disturbance. The propagation characteristics of sea-level changes have been studied using spectral analysis by several investigators (ENDo, 1968; ISOZAKI, 1969; LEE and CmJNG, 1982; LIE, 1984). Their investigation areas are separated into two parts, i.e. along the Japan coast and the east coast of Korea. Table 1 is a summary of evidence for the existence of the progressive wave along the southwestern Japan Sea coast. From these reports, it is clear that sea-level variations with significant spectral peaks propagate with the coast to the right-hand side at speeds of several m s- 1, slower than that of meteorological disturbance (several tens of m s-l). However, the prominent peak periods and propagation speeds proposed by the previous studies are different, even in the same coastal area. The difference may be due to the different period of each investigation as shown in Table 1.
*Department of Ocean Engineering, Ehime University, Bunkyo 3, Matsuyama 790, Japan. tKorea Ocean Research and Development Institute, Ansan, P.O. Box 29, Seoul, Korea. 167
168
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thin lines s h o w the bottom contours in meters.
Locationsof the tide-gaugestationsare shownby fullcircles.
Here we focus our attention on the periodicity of several days in the whole southwestern Japan Sea coastal area for a 3-year period. Objectives of the present investigation are to elucidate the following areas: (1) How important are the seasonal variations of sea-level change in each coastal area? (2) What is the relationship between the sea-level variations and the meteorological disturbances? (3) What are the typical characteristics of progressive waves along each coast? In particular, it is of interest to delineate whether such waves propagate from the Korean coast to the Japan coast or not. DATA PROCESSING The locations of tidal-gauge stations in this analysis are shown in Fig. I. Tidal data, observed at the east coast of Korea at Sogcho, Mukho and Pohang, were obtained by the Hydrographic Office of Korea. For the Japan coast, Shimonoseki, Hamada, Sakai, Saigo and Maizuru data were obtained from the Japan Oceanographical Data Center (JODC). Hourly data observed during the 3-year period from 1 January 1980 to 31 December 1982 are used in order to investigate the sea-level disturbances with a period of several days. Astronomical tides and inertial oscillations contained in the observed data were filtered out by a tide killer filter (HANAWAand MITSUDERA, 1985) and then daily mean sea levels were obtained. Hourly atmospheric pressure observations taken at weather stations (operated by the Central Meteorology Office of Korea and Japan Meteorological Agency) in the vicinity of tide-gauge stations were used. Daily mean sea-level data were adjusted by the daily mean atmospheric pressure according to the hydrostatic hypothesis ( - 1 c m m b - t). It is considered that the deformation of wind speed and direction at each meteorological station are largely influenced by the local geographical condition of the observatory. On
169
Sea-level variations
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170
Y. ISODAet al.
the other hand, YANAGI et al. (1984) showed that a uniform (spatially and temporally) wind was blowing above the southwestern Japan Sea with a several hundred km spatial scale. Therefore, the sea surface wind over the study area is assumed to be-the geostrophic wind, w fv y-
1 AP x p~, ASx (1)
--fv
x --
1 AP)' Pa ASY"
where w (v~, vy) (m s - i ) is the hindcasted geostrophic velocity component; AP (mb) is the atmospheric pressure difference between two stations; AS (km) is the distance between two stations; Pa (=1.0 kg m -t) is the air density; f (=8.5 × 10 -s s -1) is the Coriolis parameter at 36°N. That is, the daily mean northward wind component was calculated from equation (1) using the atmospheric pressure difference between Pohang and Saigo, situated at the same latitude about 36°N with the distance ASx of 420 kin. The daily mean eastward wind component was estimated from the pressure data at Shimonoseki and the mean atmospheric pressure between Pohang and Saigo, and ASy = 280 km. In the present investigation, the above adjusted daily mean sea level, daily mean atmospheric pressure and hindcasted daily mean geostrophic wind are used as the basic data, and hereafter these data are referred to without "adjusted daily mean" or "daily mean".
RESULTS Seasonal characteristics o f sea-level variations
Figure 2 shows the time series of sea level at eight stations along the southwestern Japan Sea coast and of atmospheric pressure at two stations, Sogcho (northern end) and Maizuru (eastern end). The atmospheric pressure variations of these two stations have similar patterns and amplitudes with the period at several days, although the distance between both stations is about 800 km. On the other hand, it can be seen that sea-level variations at stations along the San'In coast differ from those along the east coast of Korea. The sealevel variations along the San'In coast from Hamada to Maizuru show much larger day-today variations when compared with those along the east coast of Korea. Although Shimonoseki in the Tsushima Straits is on the Japan coast side, its day-to-day variations are small and similar to those at stations on the east coast of Korea. However, the seasonal variations of sea level at Shimonoseki are very similar to those at stations along the San'In coast. Figure 3 shows the spectrum of sea level at Mukho, Shimonoseki and Sakai which represent the east coast of Korea, the Tsushima Straits and the San'In coast, respectively. The dynamic spectrum is the analytical method which expresses the dominant periods in terms of isopleths of the spectral density with time. Its detailed analytical method is as follows: (1) Sixty-four (=26) consecutive data (about 2 months) are the basic time series, comprising one group in order to calculate the power spectrum (FFT method). The next
Sea-levelvariations
171
time series delays its beginning day for 20 days from the former one. Thus, we have the 52 groups of the time series during the 3 years from 1980 to 1982. (2) A least squares linear trend is subtracted from each time series to remove the effect of low-frequency variations. (3) The power spectrum (FFT) of each series is calculated in turn. This spectral analysis, i.e. the dynamic spectrum, can represent sea-level variations from a 2- to 32-day period. Hence, Nyquist frequency is 0.5 cpd, the resolution frequency is AF = 0.0156 cpd and the degree of freedom is 4 in each spectral analysis. (4) In drawing the above dynamic spectrum the unit of spectral density is the squared amplitude of the phenomena in order to emphasize the variations with a several-day period. The interval of isospectral density is changed for each station in order to represent the peak periods of sea-level variations. It is seen that the spectral density at Shimonoseki does not peak at periods less than 10 days throughout the year and its density is lower than that of other stations (Fig. 3). The spectral density at both Mukho and Sakai presents similar seasonal patterns about peak periods. That is, their spectral density with 3- to 5-day periods is the highest from January 10 cm(mb) (A.P.}
Sogcho Maizuru (S.L.) SOgcho Mukho Pohang
Shimonoseki Hamada
Sakai Satgo Maizuru
. . .A. M . . .J. . J A S O N D I J .F. M ..A . .M . J ]J .F. .M. .A. .M. .J. . J A S O N D I J .F. M
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1982
Fig. 2. Time seriesof dailymeansea levelat all stationsand atmosphericpressure at Sogchoand Maizurufrom 1980to 1982.
172
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Fig. 3. D y n a m i c s p e c t r u m of sea level at M u k h o , S h i m o n o s e k i a n d Sakai. Sixty-four c o n s e c u t i v e d a t a ( a b o u t 2 m o n t h s d a t a ) is a t i m e series, which is o n e g r o u p in o r d e r to c a l c u l a t e the p o w e r s p e c t r u m (FFT). T h e next t i m e series delays its b e g i n n i n g d a y for 20 days f r o m the f o r m e r one. This d y n a m i c s p e c t r u m e x p r e s s e s the c a l c u l a t e d s p e c t r a l d e n s i t y of 52 g r o u p s from 1980 to 1982.
to April in 1980 and 1981. In 1982, the high spectral density at Sakai in this season exists at high frequency, i.e. around a 5-day period, and it is not clear at Mukho. On the other hand, this spectral peak disappears from May to August when the variability is at a minimum. From September to December, a broad peak exists at a 3- to 10-day period. Relationship between sea level and meteorological disturbances ISOZAKI (1969) and ENDo (1968) suggested that sea-level variations along the Japan coast with a period of several days were caused by meteorological disturbance with the same period. The relationship between sea level and meteorological disturbances, i.e. atmospheric pressure or wind variations, are investigated using the dynamic spectrum analysis. Figure 4 shows the dynamic spectrum of atmospheric pressure at Shimonoseki and coherence-squared variations between sea levels shown in Fig. 3 and atmospheric pressure at Shimonoseki. Here, as the atmospheric pressure variation at each station along the southwestern Japan Sea coast has very similar properties, those variations are represented
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174
Y. ISODA et al.
by that of Shimonoseki. As a measure of statistical significance, 95 and 90% confidence limits of coherence-squared values are 0.78 and 0.68, respectively. The dynamic spectrum of atmospheric pressure shows that no significant spectral peaks exist from May to August, while there are spectral peaks with a period of several days present in the other seasons. Such a seasonal pattern is similar to that of sea level at Mukho and Sakai shown in Fig. 3. Therefore, sea-level variations may be affected by meteorological disturbances. However, the coherence-squared value is low at each station. This result implies that the phase of atmospheric pressure variations is not fixed to that of sea-level variation and it is suggested that sea-level variations cannot be generated effectively by atmospheric pressure variations. Although wind variations have the same periodicity as the atmospheric pressure variations, the phase of wind variations is not necessarily equivalent to that of atmospheric pressure variations. This is because each cyclone and anticyclone take different courses above the Japan Sea. Figure 5 shows the dynamic spectrum of each wind component and the coherence-squared variations among various pairs of seaqevel and wind components. The northward wind component, i.e. the component along the Korean coast, spectrum has a peak at a period of more than 20 days in winter. It is suggested that this low-frequency variation may be concerned with the winter monsoon from the Asian Continent. The variations of eastward wind component, i.e. the component along the San'In coast, occur at periods of 10 days or less. These high-frequency wind variations are very similar to the seasonal pattern of sea-level variations at Mukho and Sakai given in Fig. 3. This relationship is the same as the relationship to atmospheric pressure. However. a significant coherence with a prominent peak period appears in the case of the relationship between wind and sea level. At Mukho, the high coherence distributions of both wind components are very similar to each other. Sea-level variations at Shimonoseki have apparently high correlations with the northward wind component, and those at Sakai have high correlations with the eastward wind component. We suggest that the seaqevei variations along the southwestern Japan Sea coast can be interpreted fairly well, as a wind-generated phenomenon, although sea-level response to wind direction differs at each coastal area. Figure 6 shows the phase variations of wind vs sea level with the coherence-squared value higher than 0.4 at each station. Considering an infinitely long coast, sea level will respond mainly to the Ekman transport induced by the alongshore wind component. The wind component which induces the rise of sea level due to the onshore Ekman transport at each coast is positive. Therefore, a positive phase angle shown in Fig. 6 denotes a lead of wind variation. The phase angle for Mukho suggests that sea level has a different response to each wind component although there are similar coherence variations to both wind components. The phase variations around 90° are dominant for the eastward wind component and 0° to 45° phase angles are dominant for the northward wind component at Mukho. The phase angle with ~ gh correlation for both Shimonoseki and Sakai shows the range of 0° to 45° is dominant. These results imply that the wave may be generated only by the alongshore (eastward) wind component and propagated along the San'In coast. However, we cannot conclude whether the sea-level variations along the east coast of Korea are generated by the offshore (eastward) or alongshore (northward) wind component variations. The sea-level variations at Shimonoseki are related to the offshore (northward) wind component variations. In other words, its relationship is similar to those of Mukho in the east coast of Korea although Shimonoseki faces the Tsushima Straits. Such relations between sea level
Sea-level variations
175
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Propagation characteristics of sea-level variations Phase speeds were calculated from phase lags for coherence-squared values of more than 0.5. We made the cross-correlation analysis at the following four coastal regions due
176
Y. ISOOA et al.
'to the difference in bottom topography: (1) the east coast of Korea (Sogcho to Pohang), (2) from the Korean coast to the Japan coast (Pohang to Hamada), (3) along the western (Hamada to Sakai) and (4) eastern region (Sakai to Maizuru) of the San'In coast. The San'In coast was divided into two small regions due to the difference in shelf topography; the shelf width at the western region is wider than that at the eastern region (Fig. 1). The cross-correlation analysis period is classified into three periods, January to April, May to PHASE
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177
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August and September to December, because the prominent peak periods of sea level depend upon the period as shown in the previous section. The estimated propagation speeds for each pair of stations are summarized in Fig. 7. The propagation characteristics of the four regions are as follows: the frequency band with wave propagation characteristics is a 2.5- to 6-day period and there is no remarkable difference in propagation speeds due to the difference in the prominent peak period and the cross-correlation analysis seasons. The former characteristic suggests that the generated waves are non-dispersive. The latter suggests that such waves may be little affected by the seasonal change of the stratification. The phase of sea-level variations along the east coast of Korea propagates southward at a speed of 20-90 m s- 1. The phase of sea-level variations along the San'In coast propagates slower than that of the Korean coast. The sea-level variations in the western and eastern regions of the San'In coast propagate eastward at a speed of about 14 and 5 m s -1, respectively. It is found that these propagation speeds are positive in each coastal area,
178
Y. 1SODAet al.
'that is, this propagation characteristic is consistent with that of the theoretical continental shelf wave or Kelvin wave, which always propagates with the coast on the right-hand side in the northern hemisphere. On the other hand, the propagation speed between the Korean coast and the Japan coast seems to be about 6 m s - ~from Hamada to Pohang, i.e. with the shallow area to the left-hand side. The direction of such phase propagation cannot be explained by the propagation of a shelf or Kelvin wave. Therefore, this observed wave propagation between the Korean coast and the Japan coast may be apparent due to the different propagation characteristics at each coastal area or the topographic effect of the Tsushima Straits. From the results of sea-level analysis, the existence of waves which propagate continuously between the Japan and Korean coastal area is not found. To investigate the type of prominent wave at each coastal area, the theoretical propagation speeds of free waves, i.e. the external Kelvin wave (a), the internal Kelvin wave (b) and the shelf wave (c), are calculated. (a) The external Rossby radius deformation over the shelf is about 2 = \,~,,h(f = 450 kin, where g = 9.8 m s-2 is the gravitional acceleration, h = 150 m the mean depth over the shelf and f = 8.5 x 10 -5 s -1 the Coriolis parameter. Since this radius deformation 2 is several times as large as the shelf width, the depth off the shelf edge (about H = 2000 m) is related to the propagation speed of the external Kelvin wave. Then, its propagation speed is about Ce = V~gH = 140 m s -~. (b) The permanent pycnocline always exists at about 150 m depth between the Japan Proper Cold Water and the Tsushima Warm Water. Therefore, the internal Kelvin wave is possibly trapped at the shelf edge where the pycnocline intersects the shelf slope. Its propagation speed is calculated by Ci = X/~g&ph h ' / H = 1.6 m s -1 , where h(= 1850 m) and h'(=150 m) are the thickness of the lower and upper layers, respectively, Ap (=2 x 10 -3) is the difference in density between both layers and H(=2000 m) is the total depth. (c) Since the coast is an important factor for the wind-induced shelf wave to supply the water column with the vorticity, this type of wave may be trapped by the bottom slope near the coast, The properties of coastal trapped waves when the pycnocline intersects a sloping bottom were studied by KAW~,BF~(1982) using a two-layer model. He denoted that the properties of the upper (lower) shelf wave were almost unaffected by the existence of a lower (upper)-layer slope. Therefore, the barotropic shelf wave trapped by the upper bottom slope is considered. The bottom topography profiles shallower than about 1000 m depth off the coastal areas A, B and C shown in Fig. 1. are approximated by the exponential function as shown in Fig. 8a. The actual bottom topography is represented by a solid line and the model topography by a dotted line. Using the linear theory of barotropic shelf wave with the exponential depth (BuCHWALDand ADAMS,1968), the obtained dispersion relations for the lowest three modes are shown in Fig. 8b. As the observed wave in a forced region is modulated by the wind-forced wave, it cannot represent the true propagation speed of the free wave. For example, two waves with the same frequency, w, unit amplitude and different wavenumbers, kl, k2, are considered. One is the wind-induced free wave (kl) and the other is the wind-forced wave (k2) with the same scale of meteorological disturbances. This problem was treated by GILL and SCHUMANN (1974). They have shown that the amplitude of each wave satisfies a simple, first-order wave equation. That is, the observed (kob: wavenumber) wave has the relationship
Sea-level variations
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sin (kob x-wt) = sin (klx-wt) + sin (kex-wt) = 2cos ((kl - k~)xl2) sin ((kl + k2)xt2 - wt)).
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Therefore, the observed wave propagation speed Cob is Cob = w/kob = 2w/(kl + k2).
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Equations (4) and (5) show that for equal amplitude of the directly forced and free wave the observed wave propagation speed has a value from one to two times that of the free wave. Thus, when we infer the existence of waves in a forced region from the observed phase propagation speed, we must pay attention to the above wave property. The internal Kelvin w.ave in this study area has a theoretical propagation speed from 1.6 to 3.2 m s -1. However, such slow wave propagation is not observed at every coastal area. We suggest that the sea-level variations only along the San'In coast are first mode shelf waves as shown in Fig. 8. The sea-level variations along the Korean coast cannot be so easily interpreted. The propagation speed of the free wave suggested from the observations is 10-90 m s-1, which is the intermediate speed between the theoretical continental shelf wave (a first mode wave has about 1.5 m s - t phase velocity in the non-dispersive region) and an external Kelvin wave (about 140 m s-t). Sea-level variations in the Korean coastal area have a complicated response to wind due to the existence of unspecified waves and the high correlation in each wind component. DISCUSSION AND CONCLUSION Sea-level data obtained along the southwestern Japan Sea coast from 1 January 1980 to 31 December 1982 have been analysed using the method of dynamic spectral analysis. The results indicate that the seasonal variations of sea level can be roughly divided into three seasons. One has its prominent peak period at 3-5 days from January to April. In the second season significant sea-level variations disappear from May to August. The season from September to December has a broad peak at 3-10 days. These variations of sea level are highly coherent with the hindcasted geostrophic wind variations, while incoherent with the atmospheric pressure variations. This implies that the sea-level variations in the southwestern Japan Sea coast are caused by the prominent peak period of wind variations with the period of several days. The wind-induced sea-level variations in the frequency band from 2.5 to 6 days propagate non-dispersively. However, the progressive waves along the San'In coast and Korean coast exist independently. The existence of waves which propagate continuously between each coastal area cannot be found from this sea-level analysis. By comparing the theoretical wave phase speeds with the observed propagation speeds, we conclude that a first mode shelf wave exists along the San'In coast. This shelf wave is generated by the east-
Sea-level variations
181
west wind variations, i.e. the alongshore wind c o m p o n e n t , and begins to propagate from the exit of the Tsushima Straits situated at the westorn end of the San'In coast. This is because sea-level variations at Shimonoseki facing the Tsushima Straits have relatively lower amplitude and high correlation with the n o r t h - s o u t h wind variation. Although sealevel variations along the Korean coast have a tendency to p r o p a g a t e from north to south, the wave type cannot be specified from its propagation speed. T h e observed propagation speed is intermediate between the theoretical shelf wave and the external Kelvin wave. Moreover, such sea-level variations have a complicated response to wind due to high correlation with both the alongshore and offshore wind component. The results of this study differ from those of LEE and CHUNG (1982) and LIE (1984), especially regarding the observed propagation speed. One possible reason for this m a y be that since the shelf topography along the east coast of K o r e a is relatively steep (Fig. 1), the phase speed of an expected free shelf wave will be very slow, i.e. less than 1.5 m s -1 (Fig. 8). If such a wave exists along the K o r e a n coast, the propagation time from Sogcho to the Tsushima Straits, about 400 km, is m o r e than 3 days. Therefore, it is possible that a shelf wave generated from the f o r m e r meteorological disturbance remains along the Korean coast when a new shelf wave is generated. In the above case, sea-level variations along the Korean coast will b e c o m e very complicated due to mixing between forced and free waves. In this case, a wave-generated area is an important factor, which we cannot detect in this study. W e plan to investigate the wave-generated area and propagation of shelf waves using data f r o m several m o r e close stations along the K o r e a n coast in the near future. Although sea level along the soutwestern J a p a n Sea coast has the variations as described above, the current variations over the shelf m a y not necessarily oorrespond to such sealevel variations at the coast. In fitting the phase speeds of barotropic shelf waves to the data at Taisha Bay in the San'In coast, YANAGI et al. (1984) found that the second m o d e of shelf waves was as dominant as current variations. Such higher m o d e dominance of the current has also been denoted off the Fukushima coast by KOBOTA et al. (1981), off the Oregon coast by HSIEH (1982) and off the east coast of Australia by CHURCH et al. (1986) and FREELAND et al. (1986). These studies denote that the spatial and temporal flow distributions over the shelf due to the wind-induced shelf wave cannot be sufficiently predicted only by the information of sea-level variations at the coast. We will study the characteristics of shelf waves along the southwestern J a p a n Sea coast with the use of sea level and current data in the near future. Acknowledgements--The authors express their sincere thanks to Dr H. Takeoka and Mr H. Akiyama of Ehime University for their helpful discussion and Mr O. Miura for his assistance in data analysis. The data processing was carried out on a FACOM M-360 AP of the Computer Center of Ehime University.
REFERENCES BUCHWALDV. T. and J. K. ADAMS(1968) The propagation of continental shelf wave. Proceedingsof the Royal Society, A365, 235-250. CHURCHJ. A., J. F. HOWARD,H. J. FREELANDand R. L. SMITH(1986) Coastal-trapped waves on the East Australian continental shelf. Part 1, Propagation of modes. Journal of Physical Oceanography, 16, 19291943. ENDOH. (1968) Spectral analysis of daily sea level records along the coast of Japan. Report of Hydrographic Researches, 4, 5-19.
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FREELAND H. J., F. M. BOLAND,J. A. CHURCH, A. J. CLARKE. A. M, G. FORBES,A. HUYER,R. L. SMITH, R. O. R. Y. THOMPSONand N. J. WHITE (1986) The Australian coast experiment. A search for coastal-trapped waves. Journal of Physical Oceanography, 16, 1230-1249. GILL A. E. and H. Schumann (1974) The generation of long shelf waves by the wind. Journal of Physical Oceanography, 4, 83-90. HANAWA K. and H. MITSUDERA (1985) O n the data processings of daily m e a n values of oceanographical data. Note on the daily m e a n sea-level data. Bulletin of Coastal Oceanography, 23, 79-87. HSIEH W. W. (1982) Observations of continental shelf waves off Oregon and Washington. Journal of Physical Oceanography, 12, 887-896. ISOZAKII. (1969) A n investigation on the variations of sea level due to meteorological disturbances on the coast of Japan islands (3), O n the variation of daily m e a n sea level. Journal of the Oceanographical Society ofJapan, 25, 91-102. KAWABE M. (1982) Coastal trapped waves in a two-layer ocean: Wave properties when the density interface intersects a sloping bottom. Journal of the Oceanographical Society of Japan, 38, 115-124. KUBOTA M.. K. NAKATA and Y. NAKAMURA(1981) Continental shelf wave off the Fukushima coast, Part 1, Observation. Journal of the Oceanographical Society of Japan, 37, 267-278. LEE J. H. and Y. CHUNG (1982) Continental shelf waves off the eastern coast of Korea. La Mer, 20, 169-180. LIE H. J. (1984) Coastal current and its variation along the east coast of Korea. In: Ocean hydrodynamics of the Japan and East China Sea, T. TCHIYE, editor, Elsevier, A m s t e r d a m , pp. 399-408. SHOJI D. (1961) O n the variation of the daily m e a n sea levels along the Japan islands. Journal Of the Oceanographical Society of Japan, 17, 21-32. YANAGI T., Y. ISODA and N. KODAMA(1984) The long period waves on the San'In coast (in Japanese). Bulletin of the Disaster Prevention Institute, Kyoto University, 27, 611-620.