A study of internal waves in the China Seas and Yellow Sea using SAR

*Corresponding author. Fax: 886-2-24631764.E-mail address: [email protected] (M.-K. Hsu)

Continental Shelf Research 20 (2000) 389}410

A study of internal waves in the China Seasand Yellow Sea using SAR

Ming-Kuang Hsu!,*, Antony K. Liu", Cheng Liu#

!Department of Oceanography, National Taiwan Ocean University, Keelung, Taiwan, Republic of China"Oceans and Ice Branch, NASA/Goddard Space Flight Center, Greenbelt, MD, USA

#Department of Applied Physics, Chung Cheng Institute of Technology, Taiwan, Republic of China

Abstract

Synthetic aperture radar (SAR) images from ERS-1 and ERS-2 have been used to study thecharacteristics of internal waves in the East China Sea. Rank-ordered packets of nonlinearinternal waves in the East China Sea are often observed in the SAR images, especially in thenortheast of Taiwan. In this region, the internal wave "eld is very complicated, and itsgeneration mechanisms include the in#uence of the tide and the upwelling, which is induced bythe intrusion of the Kuroshio across the continental shelf. The internal wave distributions in theEast and South China Seas have been compiled based on the SAR observations from satellites.The Kortweg}deVries (KdV) type equation has been used to study the evolution of internalwave packets generated in the upwelling area. Depending on the mixed layer depth, bothelevation and depression waves can be generated based on numerical simulations as observedin the SAR images. The merging of two wave packets from nonlinear wave}wave interaction inthe Yellow Sea has been observed in the SAR image and is demonstrated by numericalresults. ( 2000 Elsevier Science Ltd. All rights reserved.

Keywords: Internal waves; Solitons; Upwelling; Wave}wave interaction; China Seas; Yellow Sea

1. Introduction

The East China Sea is one of the adjacent seas of China and it is rich in naturalresources. The Kuroshio is the major western boundary current of the Paci"c andits main body passes through the East Coast of Taiwan. Fig. 1 shows the bottom

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0278-4343/00/$ - see front matter ( 2000 Elsevier Science Ltd. All rights reserved.PII: S 0 2 7 8 - 4 3 4 3 ( 9 9 ) 0 0 0 7 8 - 3

Fig. 1. The bathymetry and the internal wave distribution in the East China Sea.

topography in the East China Sea and the Kuroshio area. A branch of the Kuroshiopasses the Luzon Strait entering the South China Sea. Fig. 2 shows the bottomtopography of this area and the northeast region of the South China Sea. As currentsin the East China Sea and Kuroshio interact with each other, materials in the waterare exchanged. This exchange plays an important role in de"ning the East China Seaas a biogeochemical system. A permanent upwelling area was found northeast ofTaiwan, which is induced by the intrusion of the Kuroshio across the continental shelf(Hsueh et al., 1993). The Kuroshio Edge Exchange Process (KEEP-I and KEEP-II)projects intend to study these exchange processes (Liu et al., 1992). The Kuroshiofronts and cold eddies in the upwelling region have been observed by AVHRR images(Liu et al., 1992) and SAR images (Hsu et al., 1995).

The tidal #ow over topographic features such as a sill or continental shelf ina strati"ed ocean can produce nonlinear internal waves of tidal frequency and hasbeen studied by many investigators (Sandstrom and Elliott, 1984; Apel et al., 1985;Apel, 1995). Their observations provide insight into the internal wave generation

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390 M.-K. Hsu et al. / Continental Shelf Research 20 (2000) 389}410

Fig. 2. The bathymetry and the internal wave distribution in the northeast of South China Sea.

process and explain the role they play in the transfer of energy from tides to oceanmixing. These nonlinear internal waves were apparently generated by internal turbu-lent mixing or baroclinic shear instability over bottom features. It is clear that theinternal waves play an important role in the KEEP project, because the internal wavesinduced circulation, breaking, and sediment transport in this area in#uence the localmixing signi"cantly. Therefore, the evolution of internal waves and wave}waveinteraction in the northeast of Taiwan needs to be studied, in order to understand theexchange of materials between the East China Sea and the Kuroshio.

It is well known that internal waves have surface signatures recognizable in satelliteSAR images (Fu and Holt, 1982; Alpers, 1985). The SAR images have been used tostudy the characteristics of internal waves northeast of Taiwan from Russian Almaz-1SAR (Liu et al., 1994) and from the First European Remote sensing Satellite (ERS-1)SAR (Liang et al., 1995; Mitnik et al., 1996; Liu et al., 1998). For example, Fig. 3 isa typical ERS-1 SAR image (100]100 km) of northeast of Taiwan collected on May10, 1994, showing complicated internal wave patterns. Rank-ordered packets ofinternal solitons near the edge of continental shelf are observed in the SAR images.Based on the assumption of a semidiurnal tidal origin, wave speed can be estimated


M.-K. Hsu et al. / Continental Shelf Research 20 (2000) 389}410 391

Fig. 3. ERS-1 SAR image (Copyright ESA) of northeast of Taiwan collected on May 10, 1994, at 02:25 UTCshowing complicated internal wave pattern (marked by IW). The Kuroshio boundary is shown on theup-right side of the SAR image (marked by KF). The SAR image is 100 km]100 km in size and the scenecenter is 25312@N, 122311@E.

and is consistent with the internal wave theory. The Kuroshio boundary is clearly seenon the upper right side of the SAR image. At the right-hand side of boundary is thewarm Kuroshio water with high salinity and on the left-hand side is the cool EastChina Sea water with low salinity.

Most of the internal waves that have been observed are of the depression type.Serebryanyy (1990) in the Sea of Japan has measured elevation internal waves. Basedon single mooring measurements, internal wave trains of di!erent polarity have beenobserved and separated by 12 h. Change of polarity in internal waves was alsoobserved by Salusti et al. (1989) in the eastern Mediterranean Sea using a thermistorchain and by Liang et al. (1995) from a SAR image. Liu et al. (1998) demonstrated bynumerical simulation that the elevation internal waves might be converted froma depression internal wave. When the depression internal waves propagate on shore,



the bottom layer becomes thinner. After these waves pass through a critical depth,where the thickness of the mixed layer is the same as the bottom layer, a depressionsoliton "rst disintegrates into a wave packet and then converts to the elevationinternal waves. The e!ect of variation of water depth on the evolution of nonlinearinternal wave packets has been linked to the observations from the SAR images.

In fact, rank-ordered packets of internal solitons in the East China Sea have beenobserved in many SAR images. The line drawings of these internal waves shown inFigs. 1 and 2 are compiled from hundreds of ERS-1/2 and Space Shuttle SAR imagesin the East and South China Seas from 1993 to 1997, respectively. Based on theinternal wave distribution map in Fig. 2, most of the internal waves in the northeastpart of South China Sea are propagating westward. These internal waves are gener-ated from the shallow topography or sills in the Luzon Strait (Liu et al., 1998) or fromthe shelf break in the South China Sea. The wave crest can be as long as 200 km withamplitude of 100 m, due to the strong current from the Kuroshio branching out intothe South China Sea. Compared with the internal waves in the South China Sea, theinternal waves in the East China Sea are relatively small in scale, but more complic-ated in their directions of propagation and from the generation sources on shelf break(Fig. 1). In the northeast of Taiwan, the common interested area of KEEP project,the internal waves are propagating in most all of the directions. They may not begenerated by a simple mechanism from the edge of the continental shelf such as thecase in the New York Bight (Liu, 1988). They have complicated evolution on the shelfsuch as wave re#ection, breaking of internal waves, variation of bottom topography,shoaling, and wave}wave interaction due to multiple sources. Based on the SARimages collected over the East China Sea, internal wave}wave interactions have beenobserved in many places. Zhang et al. (1997) based on the photographs from thespace shuttle o! the coast of South-west Africa has reported such wave}waveinteraction.

In this paper, the SAR imaging mechanisms of internal waves and the procedures ofprocessing ERS-1 SAR images will be brie#y described "rst. Then, the selective sets ofSAR images in the East China Sea are presented to discuss the internal wavegeneration mechanisms in Section 3. The generation mechanisms include in#uences ofthe tide and the Kuroshio for the formations of both elevation and depression internalwaves in di!erent ocean environment conditions. The internal wave evolution model,which is represented by the nonlinear Kortweg}deVries type equation, are describedin Section 4. In Section 5, the internal wave generations of both depression type andelevation type by upwelling are simulated by numerical method in di!erent environ-mental conditions. Finally, the wave}wave interaction of internal waves in the YellowSea observed in a SAR image is studied in detail to show the merging of wave packets.

The original "ndings of this study are to demonstrate the generation of bothdepression and elevation internal waves by upwelling under di!erent mixed layerconditions, and to show the wave}wave interaction observed from the satellite inorder to interpret the ship measurements. Both wave generation by upwelling in theEast China Sea and wave}wave interaction in the Yellow Sea have never been studiedand presented before in any literatures. Furthermore, the internal wave distributionmaps for the East and South China Sea and Yellow Sea based on more than 300



satellite images are the most recent and important information for future planning ofinternal wave related "eld tests.

2. SAR observations

European Space Agency launched ERS-1 and ERS-2 satellites in 1991 and 1995,respectively. For ERS-1and ERS-2 (ERS-1/2), in the image mode, SAR obtains stripsof high resolution imagery approximately 100 km in width, 250 km to the right of thesub-satellite track. A spatial resolution is 26 m in range (across track) direction andbetween 6 and 30 m in azimuth (along track) direction (Vass and Battrick, 1992). Intheir primary orbit, the revisit cycle for ERS-1/2 SAR is 35 days. The ERS-1/2 SARimages used in this paper were acquired by the Center for Space and Remote SensingResearch (CSRSR) at the National Central University (NCU) in Taiwan.

SAR maps the sea surface roughness through Bragg scattering from the capillarywaves and short gravity waves. The relation is

K"

j2 sin h

, (1)

where K and j are the wavelength of capillary waves and radar respectively, and h isthe local incidence angle. For ERS-1/2 SAR (c band), j"5.66 cm, and h is between19.5 and 26.63 with VV polarization. For the ocean, it is sensitive to the waves withwavelength of 8.3}6.5 cm. The threshold wind speed u

.*/, which is needed to generate

the resonant Bragg waves, depends on radar frequency and sea surface temperature.For ERS-1/2 SAR the u

.*/is about 3.2 m/s at a height of 10 m above the ocean surface

(Donelan and Pierson, 1987).Each ERS-1/2 SAR scene covers an area of 100 km]100 km. The digital SAR

image has approximately 8000 pixels in column and 8000 pixels in row (with a pixelsize of 12.5 m]12.5 m). In order to enhance the meso-scale features and to reduce thespeckle noise (to increase the signal-to-noise ratio), the pixel size of original imageswere increased by an 8]8 block average (to a pixel size of 100 m]100 m). Threekinds of correction have been applied during image processing to get quantitativeestimates of the Normalized Radar Cross Section (NRCS) variations. Range correc-tion compensates the decrease of the NRCS with the increase of incidence angle. Thevariations of transmitter power are compensated by radiometric correction. At last,antenna correction takes account of the shape of the antenna pattern. The corre-sponding correction programs have been provided by the CSRSR of NCU.

Fig. 4(a) shows the ERS-1 SAR image of northeast of Taiwan collected on July 23,1994, at 02:26 UTC with many internal wave packets clearly observable. The darkarea on the northeast of Taiwan is an upwelling zone induced by the Kuroshiointrusion on the continental shelf. On July 22, 1994 at 08:03 UTC, approximately 16 hbefore the SAR image was acquired, a sea surface temperature (SST) map derivedform NOAA-11 AVHRR (channel 4) image was obtained as shown in Fig. 4(b).Fig. 4(b) shows a cold eddy and a narrow band connecting a colder pool of water near



Fig. 4. (a) ERS-1 SAR image (Copyright ESA) of northeast of Taiwan collected on July 23, 1994, at 02:26UTC showing internal wave packets in the upwelling area. The black block northeast of Taiwan is thelocations of upwelling. The SAR image is 100 km]100 km in size and the scene center is 25320@N, 121357@E.(b) NOAA-11 AVHRR sea surface temperature image on July 22, 1994 at 08:03 UTC showing a cold eddyin the upwelling area and a narrow band connecting a colder pool of water near the western Kuroshioboundary.

the western Kuroshio boundary. The cold eddy (dark area) northeast of Taiwan canbe identi"ed as the core of upwelling in this SST map. Since the upwelling water ismuch colder than the water in the surrounding area, the sea surface is smoother in theupwelling area because of the stable atmosphere boundary layer (Vachon et al., 1992).The dark appearance of surface "lm on radar images is due to the smoothing ofthe ocean surface caused by the damping of short backscattering waves. Therefore, theupwelling area has less backscattering and is dark in the SAR image.

The essential element of the surface e!ects is the interaction between the internalwave-induced surface current "eld and the wind-driven ocean surface waves. For alinear SAR system, the variation of the SAR image intensity is proportional to thegradient of the surface velocity, or to the strain rate. The proportionality depends onradar wavelength, radar incidence angle, angle between the radar look direction andthe internal wave propagation direction, azimuth angle, and the wind velocity. In theSAR images (Figs. 3 and 4(a)), a depression internal wave packet can be identi"ed asa bright band followed immediately by a dark band. The schematic diagram of



Fig. 4. (Continued.)



Fig. 5. Schematic diagram of elevation internal wave generation by upwelling. The vertical pyanoclinedisplacement in the upwelling area is induced by the intrusion of Kuroshio and evolves into a packet ofsolitons initiated by tide.

interaction of internal waves, induced surface current with wind waves, and theresultant SAR image intensity variations can be found in (Liu et al., 1998). For thehigh wind speed condition, the internal wave signal maybe too weak to be observed byradar due to low signal-to-noise ratio. When the internal waves propagate in thecrosswind direction, the wave-current interaction is also relatively weak, and so is theradar backscattering for SAR observation. The strain rates have been calculated forthe internal wave packets in the East China Sea (Liu et al., 1998) and their values areconsistent with the observed data from New York Bight internal waves (Liu, 1988).

3. Generation mechanisms

The tidal #ow over topographic features such as a canyon, around an island, or acontinental shelf in a strati"ed ocean can produce depression internal waves in deepwater as also observed in the Taiwan area. Most of the internal waves in the East



China Sea, especially in the summer, observed from the SAR images are depressioninternal waves. In the summer, the mixed layer is often found to be thinner ascompared with the bottom layer on the continental shelf. However, in the fall/winter,the mixed layer can be thicker than the bottom layer, especially in shallow water dueto strong wind condition. Then, the elevation internal waves can be generated asreported by Liang et al. (1995) and Liu et al. (1998). In the north of Taiwan, twointernal wave packets separated by approximately 30 km were identi"ed on an ERS-1SAR image collected on October 21, 1992. Each wave packet is characterized bya dark band followed immediately by a bright band, which is di!erent from the surfacesignature of depression waves, a bright band followed immediately by a dark band(Liu et al., 1998). This reversal of surface signature indicates the existence of underly-ing nonlinear elevation internal waves. The elevation internal waves may be convertedfrom a depression internal wave through the critical depth as reported by Liu, et al.(1998). However, these elevation waves can be also generated directly when theenvironmental conditions are favorable.

Because of the bottom topography, the Kuroshio intrudes onto the continentalshelf immediately after passing the northeast tip of Taiwan. A cold water anomaly,which manifests as upwelling of the subsurface Kuroshio water has been frequentlyobserved at the shelf break of the East China Sea to the north of Taiwan (Lin et al.,1992). A schematic diagram of generation process of elevation internal wave withupwelling is proposed in Fig. 5. The upwelling induced by the Kuroshio intrusion atthe shelf break may have a dooming e!ect on the bottom of mixed layer. Thedisturbance of doomed area with upward displacement of the pycnocline is thendriven by the semi-diurnal tide onto the shelf and evolves into a rank-ordered wavepacket. In the shallow water, when the mixed layer is thicker than the bottom layer,a rank-ordered elevation wave packet may be generated. However, if the mixed layeris thinner than the bottom layer, a depression wave packet may evolve. Based ona simple internal wave model, the numerical simulations of wave generation fromupwelling for both environmental conditions are demonstrated in the followingsection.

4. Wave evolution model

The evolution of solitons is based upon the balance of nonlinear e!ects with thedispersive e!ects. A solitary wave theory that describes the evolution of nonlinearinternal waves has been developed and expanded by Liu et al. (1985). It includes thee!ects of vertical shear, variable bottom topography, radial spreading, and dissipationby Liu et al. (1985) for the Sulu Sea internal soliton study (Apel et al., 1985). Theevolution of nonlinear internal waves can be simulated numerically by solving theKortweg}deVries-type equation with varying coe$cients corresponding to the chang-ing environments as demonstrated by Liu (1988) and Liu et al. (1985, 1998). Thedissipation e!ects on solitary wave evolution are important in the shallow waterowing to internal wave breaking and strong turbulent mixing.



Liu (1988) has formulated the evolution of nonlinear internal wave trains ona continental shelf. The evolution equation of wave amplitude A(x, t) with variablecoe$cients is

At#C

0A

x#aAA

x#bA

xxx#cA!1

2eA

xx"0, (2)

where the parameters a, b, c and e are the coe$cients for the nonlinear, dispersion,shoaling, and dissipation e!ects.

For a two-layer system where H1

and H2

represent the thickness of the mixed layerand bottom layer, the nonlinear and dispersion coe$cients are

a"3

2

H1!H

2H

1H

2

C0, (3)

b"16

H1H

2C

0, (4)

and the linear wave speed is given by

C0"S

*ogH1H

2o(H

1#H

2), (5)

where g is the gravity constant, o is the density of water and *o is the densitydi!erence between two layers. The evolution of solitons is based upon the balance ofnonlinear e!ects with the dispersive e!ect. Note that a sign changes when the waterdepth across the critical depth H

1"H

2(turning point). The sign of nonlinear term

depends on the wave amplitude; a depression wave has the opposite sign of anelevation wave in amplitude. When the mixed layer depth is thinner than the bottomlayer, H

1(H

2, only depression waves can be originated. If the mixed layer is thicker

than the bottom layer, H1'H

2, only the elevation waves can be evolved. Therefore,

the elevation waves can be evolved near shore because the bottom layer is thinnerthan the mixed layer over the sloping shelf. The coe$cient for the shoaling e!ect, c,is in the order of !2]10~5 S~1 (Liu, 1988). Liu (1988) and Liu et al. (1985, 1998)reported a horizontal eddy viscosity for solitons of e"1}10 m2/s. A numericalapproach using Fornberg's pseudo-spectral method (Liu et al., 1985) has been de-veloped to solve the evolution equation. A parametric study for various environ-mental conditions has been carried out to demonstrate and to assess the nonlineare!ects such as bottom topography, shoaling (across critical depth), and dissipa-tion/mixing on internal wave evolution (Liu et al., 1998).

5. Numerical results

Based on the internal wave model described in the last section, the numericalparametric study of wave generation from upwelling for di!erent environmentalconditions has been performed. Speci"cally, the major interest is the generation ofdepression waves and elevation waves from an upwelling region under favorable



conditions. The generation of internal waves is clearly a three-dimensional process.However, in this study, the two-dimensional model is used for the insight andimplication of this complicated generation process. Although the numerical simula-tion may not be taken as a quantitative measure, the results are de"nitely useful asqualitative interpretation for the remote sensing observations. Therefore, a series ofnumerical experiments have been performed, by solving the initial value problemdescribed by Eq. (2) with a simple upward disturbance for the upwelling area. Theinitial displacement is given by

A(x, t)"!A0

sech Ax!ct

¸ B, (6)

where A0

is the pycnocline displacement at the center of a hump, c is the phasevelocity and ¸ is the half-width of the upwelling area.

For the "rst case, an internal wave of depression generated by upwelling inducedpycnocline displacement is considered. The internal waves of depression are oftengenerated in the region where the mixed layer is thinner than the bottom layer, whichis in general the most common condition on the continental shelf. In this case, a mixedlayer thickness of 25 m (H

1"25 m) and a bottom layer of 150 m (H

2"150 m) are

chosen for simulation. The density contrast is set *o/o"10~3. An initial pro"lecorresponding to an upwelling generated hump is considered; the e!ective size of thehump area is approximately 10 km (or 2¸"6 km), and the height of the humpA

0"5 m is chosen for pycnocline displacement. At "rst, no dissipation is considered

in the simulation. The wave pro"les as a function of time (time}space plot) are shownin Fig. 6(a), where a moving frame is applied in order to keep the propagated waves inthe same window. It is shown in Fig. 6(a) that the depression internal waves are "rstgenerated at the left side of the hump area, then more waves are generated in the wavepacket. Finally, eight rank-ordered solitons of depression type are generated after27 h. Fig. 6(b) shows the results, which obtained from similar conditions with the dis-sipation coe$cient of 2 m2 s~1. By including the dissipation e!ects, such as the localincipient shear #ow instability or wave breaking, the number of waves in the wavepacket is reduced (six solitons) and the amplitudes are also decreased by 30%.

In the second case, the generation of elevation internal waves by upwelling inducedpycnocline displacement is considered for the case when the mixed layer is thickerthan the bottom layer. In this case, the thickness of mixed layer of H

1"150 m and

the bottom layer of H2"25 m are used (reversed from the "rst case). The same initial

condition corresponding to an upwelling generated hump is considered "rst withoutdissipation. The time}space plot of wave pro"les is shown in Fig. 7. In this case, theelevation internal waves are generated at the front end (on-shore side) of the upwellingarea. Then, "ve rank-ordered elevation solitons in the packet are generated after 27 h.When the dissipation e!ects are included with the dissipation coe$cient of 2 m2 s~1,the number of waves in the wave packet was decreased (three elevation solitons) andthe amplitudes of the waves are also reduced by 20%. It was suggested that theinternal wave of elevation type might be evolved from internal waves of depressiontype (Liu et al, 1998), when internal waves of depression type pass a critical depth



Fig. 6. Numerical results of generation of depression internal waves by upwelling for (a) without dissipa-tion, and (b) with dissipation coe$cient of 2 m2/s.



Fig. 7. Numerical results of generation of elevation internal waves by upwelling.

(H1"H

2). Here another possibility is suggested that an internal wave packet of

elevation type may be generated by an upwelling directly.From these simulation results, it is concluded that internal waves of both depres-

sion type and elevation type can be generated by upwelling under favorable condi-tions. They may propagate in all directions from the upwelling region, and are notnecessary limited to a shoreward direction. This is consistent with complex internalwave patterns seen on SAR images northeast of Taiwan.

Many in situ measurements had been carried out in the last two years, in order to"nd out the generation mechanisms in the northeast of Taiwan. Due to the complic-ated current "eld induced by the Kuroshio, tides, and internal waves in that area, thedata collected during the last two years were not su$cient to validate the proposedgeneration mechanism. Further in-situ measurements have been planned to interpretthe SAR observations and to calibrate the numerical simulations.

6. Wave}wave interaction

Wave}wave interactions have been observed in many SAR images of the EastChina Sea. The internal solitons are nonlinear, thus their interactions are much morecomplicated than the regular linear waves. One of the well-known phenomena is the



Fig. 8. The bathymetry and the internal wave distribution in the Yellow Sea.

phase shift when two solitons collide. In the northeast of Taiwan, the interactionpatterns are very complicated as shown in Fig. 1. In the Yellow Sea near the SouthKorea coast, the internal waves are generated from several islands, so the waveinteraction pattern is much more organized as shown in the internal wave distributionmap in the Yellow Sea (Fig. 8). Many ERS-1 SAR images had been collected duringthe shallow water acoustics experiment in the Yellow Sea in August 1996. Based onthe SAR images, there are many internal waves propagating from the Korea coast inthe southwest of Yellow Sea. Especially, during the summer time, a shallow mixedlayer of 15 m persists in the water of 100 m depth. The internal wave packets withmore than 15 solitons of equal amplitudes were observed and measured by thethermistor chain from a research ship in the Yellow Sea during the "eld test. Thesemany solitons in wave packet may be caused by the internal wave}wave interaction inthe Yellow Sea, which results in the merging of solitons to a single large internal wave.

The ERS-2 SAR image obtained on July 23, 1997 (Fig. 9) in Yellow Sea is selectedfor the wave}wave interaction study. The SAR subscene size is 50 km]50 km and itscenter location is 34331@N and 124356@E. Several internal wave packets were generated



Fig. 9. ERS-2 SAR image obtained on July 23, 1997 in the Yellow Sea shows the internal wave}waveinteraction pattern and the merging of solitons into a single large wave packet. The SAR image is50 km]50 km in size and the subscene center is 34331@N, 124356@E.

from the islands near the southwest tip of Korea Peninsula by the collision of theKorea coastal current and the semi-diurnal tides. There are at least two generationsources (islands), one from the east and the other from the northeast. Notice that thephase/front of internal wave packets are shifted and distorted in the interaction areasdue to the nonlinear wave}wave interaction. In Fig. 9, the windows A B are con-sidered as individual internal wave packets generated at an earlier time and withoutinteraction, window C shows the waves in the interaction zone, and window D showsthe merger of wave packets after the interaction. Figs. 10(a), (b), (c) and (d) show thewave spectra from the windows A, B, C, and D, respectively. In Fig. 10(c), it can beidenti"ed that there are two major wave trains propagating from the east and



Fig. 10. Wave number spectra of (a) incident waves in window A, (b) incident waves in window B, (c) wavesin the interaction zone in window C, and (d) waves after interaction in window D as indicatedin Fig. 9.

northeast with wavelengths of 405 and 650 m (broad peak) and directions of 553 and!253. The directions of these two wave packets in the interaction zone are quiteconsistent with the waves shown in Fig. 10(a) and (b) without interaction. Thedirection of the wave train shifted after the interaction, and the new direction of 203 isin between two incident wave packets without interaction. Not only has the directionshifted after the wave}wave interaction, but the number of waves in the wave packetand the amplitude of the waves are also changed. The wavelength is approximately550 m as shown in Fig. 10(d). These results are also shown in Figs. 11(a), (b) and (c),which are the sliding averages of SAR intensity along the cross section cuts indicatedby the lines L1, L2, and L3 in Fig. 9, respectively. Figs. 11(a) and (b) show the cross



Fig. 11. Cross section cuts of SAR image (a) before interaction for line L1, (b) during interaction for L2, and(c) after interaction for L3 as indicated in Fig. 9.

section before and during the interaction with two separated wave packets. Fig. 11(c)shows the cross section after the interaction and the merger of two wave packets.

This merge of wave packets may explain the measurements of 15 solitons in theYellow Sea during the "eld test in August 1996 as shown in Fig. 12. The isothermaldepth interpolated from the thermistor chain indicates these solitons have averageamplitude of 10 m. Based on in-situ measurements of the density pro"le, the linearinternal wave speed is computed from the wave model. Then, the wavelength can beestimated to be 1 km approximately. In order to demonstrate the wave}wave inter-action, a numerical calculation with two wave packets moving in the same directionis performed. In this case H

1"30 m, and H

2"40 m are used. Fig. 13 shows the

interaction of three solitons in each of packets, with the largest soliton amplitude of10 m in the second packet. After 14 h, the largest soliton takes over two small solitonsin front with a phase shift. Finally, only four large solitons survive as a single wavepacket with compatible amplitudes after 20 h. Although the wave}wave interaction inthe Yellow Sea is de"nitely a two-dimensional process, the results here may shed somelights on the merging of wave packets.



Fig. 12. Isothermal depth versus time derived from the thermistor chain measurements of internal waves inthe Yellow Sea on August 22, 1996.

7. Discussion

Many SAR images from ERS-1/2 have been collected and used to study thecharacteristics of internal waves in the East China Sea, especially in the northeast ofTaiwan (KEEP test area). Rank-ordered packets of internal solitons near the edge ofthe continental shelf have been observed in the SAR images. In this region, theinternal wave "eld is very complicated, and its generation mechanisms include thein#uence of the tide and the upwelling, which is induced by the intrusion of Kuroshioacross the continental shelf. The internal wave distributions in the Yellow Sea, EastChina Sea, and South China Seas have been compiled based on the SAR observationsfrom satellites.

The internal wave evolution model has been described based on the weaklynonlinear theory on sloping shelf in the shallow water for a two-layer system. Thegeneration of both depression and elevation waves from the upwelling on the shelf inthe KEEP area have been demonstrated by numerical simulations. In the East ChinaSea, the internal wave pattern can be very complicated when wave packets fromdi!erent sources interact with each other, such as the case in the Yellow Sea. Based onthe SAR image, the wave packet direction is shifted and wavelength is changed.



Fig. 13. Time}space plot of numerical result of wave}wave interaction to show the merge of wavepackets.

Furthermore, the merger of two wave packets from nonlinear wave}wave interactionin the Yellow Sea has been observed in the SAR image and demonstrated bynumerical results.

A SAR image provides only a snap shot of the internal wave evolution, but largespatial coverage over the "eld measurement area. Although the repeat cycle forERS-1/2 SAR is 35 days, it is clear that these internal wave observations in the EastChina Sea from SAR provide a unique resource for addressing a wide range ofprocesses. Among these, the following can be included: the generation of internalwaves by upwelling due to the Kuroshio intrusion across the continental shelf; theevolution of elevation internal waves through the critical depth; the shoaling e!ects ofvariable bottom topography on wave evolution; and wave}wave interaction.

It had been addressed that internal waves play an important role in continentalshelf dynamics. The internal waves induced circulation, breaking, and sedimenttransport in continental shelf area in#uence the local mixing signi"cantly. Therefore,the evolution of internal waves, the breaking of internal waves, and nonlinearwave}wave interaction in the northeast of Taiwan needs to be studied in more detail,in order to understand the exchange processes between the East China Sea and theKuroshio.



Acknowledgements

This work is completed during the "rst and third authors visiting NASA/GoddardSpace Flight Center and Catholic University of American (CUA) in the Spring, 1998.They wish to thank Frank H.P. Pao in CUA for the arrangement of their visit andfruitful discussions. M.-K. Hsu wishes to thank the O$ce of Naval Research for his"nancial support. C. Liu would like to thank the Minister of Education, Taiwan forsupporting him to study in US during his Ph.D. study. The authors also acknowledgeC.T. Liu of National Taiwan University for his valuable discussions and suggestions,and Ji-Xuan Zhou of Georgia Institute of Technology for providing the internal wavemeasurement in the Yellow Sea (Fig. 12). The ERS-1 SAR images collected by ESAsatellite and processed by ESA and Taiwan Ground Station are also acknowledged.This research was supported by the National Science Council (Taiwan) throughresearch grant NSC-85-2611-M-019-011 k2, National Aeronautics and Space Admin-istration and O$ce of Naval Research.

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A study of internal waves in the China Seas and Yellow Sea using SAR

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