Simulation of Water Exchange in Jiaozhou Bay by Average Residence Time Approach ) Zhe Liua, , Hao Weia,B, Guangshan Liuc, Jing Zhangd

http://www.paper.edu.cn

Estuarine, Coastal and Shelf Science 61 (2004) 25e35

Simulation of water exchange in Jiaozhou Bay by average residence time approach ) Zhe Liua, , Hao Weia,b, Guangshan Liuc, Jing Zhangd

aInstitute of Physical Oceanography, Ocean University of China, 5 Yushan Road, Qingdao 266003, China bKey Lab of Physical Oceanography, State Education Department, 5 Yushan Road, Qingdao 266003, China cOceanography Department, Xiamen University, 422 Siming Road South, Xiamen 361005, China dState Key Lab of Estuarine and Coastal Research, East China Normal University, 3663 Zhongshan Road North, Shanghai 200062, China

Received 29 November 2003; accepted 4 April 2004

Abstract

A dispersion model coupled with the Princeton Ocean Model was used to estimate the average residence time of the water in Jiaozhou Bay. The tidal simulation agreed quite well with drift experiments and water elevation observations at the Dagang tide station in the east coast of the bay. In particular, in situ measurements of 228Ra and salinity were carried out to calibrate the dispersion model. The modelled average residence time was about 52 days, ranging from less than 20 days in the deep part near the bay channel, the only passage connecting the bay to the Yellow Sea, to over 100 days in the shallow area in the northwest. The spatial diﬀerence of average residence time was controlled by tidal residual currents and the distance to the bay channel. The modelled tidal exchange rate was uneven in the bay, and consistent with 228Ra observations. The temporal evolution of the passive tracer accords with the evolution of the rain fraction after the rainstorm in August 2001. Ó 2004 Elsevier Ltd. All rights reserved.

Keywords: water exchange; dispersion model; average residence time; Jiaozhou Bay

1. Introduction Water exchange in coastal areas can be studied by box, parcel-tracking, and dispersion models (e.g., Cheng Water exchange plays a critical role in coastal and Casulli, 1982; Luff and Pohlmann, 1996; Kitheka, ecosystems (Kraufvelin et al., 2001). Coastal areas with 1997; Dong and Su, 1999a,b), with dispersion model active water exchange usually have good self-purifica- being characterized by major physical processes (i.e., tion capability. For instance, despite increased loading advection and diffusion). Some simulation results (e.g., of contaminants, rapid water exchange transports water elevation and currents) calculated from the model nutrients to the Iroise Sea and thus maintains the could be calibrated by comparison with observations. steadiness of the ecosystem in Brest Bay (Le Pape and Other aspects of model output, such as the water Menesguen, 1997). On the other hand, flow fields favor exchange curve, cannot be easily calibrated due to lack bringing in and accumulation of pollutants, and of observations. consequently deteriorate water quality. In Koljo Fjords, In this study, a dispersion model was developed and coastal eutrophication has been building up and the used to simulate the exchange processes of Passive environment is becoming worse because of slow water Dissolved Conservative Matter (PDCM) in Jiaozhou exchange, although there are no significant local sources Bay (JZB), based on the average residence time ap- of pollutants in the adjacent land-region (Rosenberg, proach (Takeoka, 1984). The model was calibrated by 1990; Lindahl et al., 1998; Nordberg et al., 2001). observations of tidal water elevation and drift experiments. Data were collected from intensive measurements of a natural radiotracer (228Ra) and the salinity change ) Corresponding author. after a sudden rainstorm in the region was also moni- E-mail address: [email protected] (Z. Liu). tored. The comparison between the two datasets and the

26 Z. Liu et al. / Estuarine, Coastal and Shelf Science 61 (2004) 25e35

model outputs helped us to directly estimate the tidal (Ding, 1992), resulting in nearly homogeneous vertical exchange rate and obtain the curve of water exchange profiles of temperature and salinity. JZB receives limited in the area. The flow chart of analysis and computation river discharge from land regions around. On the JZB is shown in Fig. 1. west coast is the Dagu River (Fig. 2) with annual mean discharge of about 7:2 ! 108 m3 (1952e1979) (Editorial Board of Annals of Bays in China, 1993), accounting for 2. Study area 84% of the total riverine discharge into JZB (Marine Environmental Monitoring Center, 1992). The stratifi- JZB is located at the west coast of the Yellow Sea cation is weak even in summer when land-source (e.g., (YS) (35(58#e36(18#N, 120(04#e120(23#E), has aver- river) input reaches its maximum (Weng et al., 1992). In age water depth of about 7 m (Fig. 2), and is a partly- recent decades, the total amount of freshwater discharge enclosed waterbody with a narrow channel between from rivers into JZB decreased considerably, according Xuejiadao and Tuandao that connects the bay with the to data from the State Oceanic Administration of China YS (Fig. 2). JZB tides induce strong turbulent mixing and the Qingdao Aquiculture Bureau (SOA and QAB,

Start

M2 tidal force at open boundary

Input Elevation Cali Drift data from bration experiments tidal gauge Princeton Calibration Ocean Model Input Input

Output Grids scheme Elevation; Topography velocities; diffusivity

Input

Input Input

Dispersion Initial Input Model Input Open boundary concentration condition field

Output

Salinity Modelled Calibration Calibration Measurement recovery concentration of of 228Ra process passive tracer

Stop

Fig. 1. This study’s ﬂow chart of analysis and computation showing the main processes such as the coupling of hydrodynamic and dispersion models, and the integration of simulation results and observations. The details are discussed in Sections 3e5. 中国科技论文在线 http://www.paper.edu.cn

Z. Liu et al. / Estuarine, Coastal and Shelf Science 61 (2004) 25e35 27

36.20°

A1 A2 A3 A4 A5 Dagu River

B1 B2 B3 B4 B5 Jiaozhou Bay DG 36.10° C1 C2 C3 C4 D1 Channel N T D2 H E3 Shandong Peninsula D3 37° D4 E2

D5 E1 36.00° 36° XJ Yellow Sea 35° Yellow Sea

120° 121° 122° E

35.90° 120.10° 120.20° 120.30° 120.40° E Fig. 2. Topography (m) of JZB, together with the sampling stations for ﬁeld observation in August 2001. Insert is the location map (lower left). The interval of water depth is 10 m. There were two stations (B3 and C2) for 228Ra isotope measurement. Around JZB, T is Tuandao, XJ is Xuejiadao, H is Huangdao, and DG is Dagang tide station (solid triangle). The dotted areas indicate the mud tidal ﬂat. The dashed line between XJ and T indicates the channel connecting the bay to the Yellow Sea.

1998). Qingdao city with total population of about 7.1 calibrating the hydrodynamic model (Fig. 3a). The million surrounds JZB. Due to the rapid economical and sampling interval of 1 h yielded 720 valid records. social developments in this region, JZB is greatly influenced by human activities, leading to increasing 3.2. Drift experiments amount of industrial, agricultural, and aquicultural input into JZB (Fan and Zhou, 1999). Red tide has Three drift experiments, Z1, Z2, and Z3, started at become a frequent event, as the bay water is eutrophied different places (Fig. 3b), yielded the Lagrangian (Environmental Bureau of Qingdao, 1999). The de- trajectories of water mass that were used to calibrate terioration of water quality in JZB led to such serious the modelled current field. The drifter, made of iron bar- ! concern of social and scientific communities that several framed 1 m 1 m sail at 3 m depth, was attached to research projects were carried out to investigate the a buoy with a nylon cable. A thin bamboo pole was mechanisms of the water exchange in this area (e.g., Sun fixed to the top of the buoy with a flashlight and a flag. et al., 1988; Zhao et al., 2002). These projects provided The trajectories of the drifter were recorded by Model the scientific background of the present work. GPSMAP230 Global Position System. In Case Z1, the drifter was launched in the bay channel at flood tide and its trajectory was recorded for 6 h. The Z2 experiment, conducted in the north of Huangdao (H in Fig. 2), was 3. Field observations, data and methods discontinued after 9 h due to severe weather conditions. In Case Z3, the drifter was deployed at high tide in the Local historical records of tidal elevation were center of the bay and the experiment lasted for 6 h. All collected in this study. Three cruises for drift experi- the trajectories are shown in Fig. 3b. ments, observing salinity and measuring 228Ra, were ac- complished during August 13e28, 2001. 3.3. Salinity recovery

3.1. Observations of tidal elevation Typhoon Taozhi that passed over JZB in August 2001 brought heavy precipitation of over 120 mm within The September 9 to October 8, 1993 tidal elevation 9 days, which accounted for nearly 1/6 of the annual data series measured by WLR7 Aanderaa tide recorder mean rainfall (732.7 mm) in this region (Editorial Board at the Dagang tide station (DG in Fig. 2), were used for of Annals of Bays in China, 1993). In the ﬁeld 中国科技论文在线 http://www.paper.edu.cn

28 Z. Liu et al. / Estuarine, Coastal and Shelf Science 61 (2004) 25e35

2.4 Tidal Elevation at Dagang tide station 2.0 observation a 1.6 simulation 1.2 0.8 0.4 0.0 -0.4 -0.8 Tidal Elevation (m) -1.2 -1.6 -2.0 -2.4 0 48 96 144 192 240 288 336 384 432 480 528 576 624 672 720 Time (hour)

N b

36.20°

date: 08-23 Z2 time: 20:20 date:08-23 time:11:35 DG 36.10° Z3 date:08-23 date:08-24 time:02:35 time:02:20

H T Z1 date:08-15 Observation time:16:30 Simulation date:08-15 time:10:30 XJ 36.00°

120.15° 120.20° 120.25° 120.30° 120.35° E Fig. 3. Results of observation and simulation of tidal elevation in Dagang tide station (1993/9/9 0:00e1993/10/8 23:00) (a) and drift experiments (August 2001) (b).

observations, salinity was measured by Seabird 911 plus where s(t) is the mean salinity of JZB at a given time (t); CTD during the 3 cruises (August 13e28, 2001). Before sb is the salinity of ‘‘seawater’’, i.e., the salinity before the cruises, the CTD sensor was calibrated at the the rainstorm. In the course of salinity recovery, s(t) National Marine Center of Standards and Metrology of gradually returned to its original value of sb, so the rain China to accuracy of 0.01, or second decimal place, for fraction fell back to 0% after the rainstorm. In order to salinity. The CTD proﬁles from 22 grid stations (Fig. 2) validate the PDCM variation (output from the disper- in each cruise were obtained in order to gain un- sion model) by using salinity data, an index of remnant derstanding of the salinity recovery after Typhoon water, P, is introduced: Taozhi. From the temporal variations of the freshwater (due f ðtÞ P ¼ ! 100% ð2Þ to the rain) fraction in the bay measured by CTD, the f ðt0Þ water exchange rate could be calculated. Assuming salinity of rainwater is zero, the rain fraction, f (t), is where f(t0) is the rain fraction at the initial time t0. The given by Zimmerman (1976) as: remnant water index, P, represents the percentage of the original rainwater remaining in JZB after the time s sðtÞ f ðtÞ¼ b ! 100% ð1Þ duration t t0. With the development of exchange sb processes, P decreased gradually from 100% to 0%, 中国科技论文在线 http://www.paper.edu.cn

Z. Liu et al. / Estuarine, Coastal and Shelf Science 61 (2004) 25e35 29 indicating that rainwater in JZB was replaced by water 3 the detecting efficiency, N the peak area, T the from the YS. counting time, Y the yield of g-ray, with s standing for the sample, b for background. The subscript ‘‘i’’ 3.4. 228Ra measurement stands for the i-th g-ray. Three g-rays were used in this study. Ra isotopes were widely used as tracers of water The tidal exchange rate was estimated by 228Ra as: movement in coastal and open oceans (cf. Kaufman ALO AHI et al., 1973; Veeh et al., 1995; Huang et al., 1997; Ghose Rt ¼ ð5Þ et al., 2000; Moore, 2000). In this study, 228Ra specific ALO activities were measured at high and low tides to where ALO and AHI are the specific activities at low and estimate the tidal exchange rate. high tides, respectively, so that (ALO AHI) is the net Water samples were collected at stations B3 and amount of exchange in one tidal cycle. C2 (Fig. 2) during August 13e24, 2001. About 440e780 dm3 of seawater was sampled from the sub- surface layer and Ra was concentrated by passing the 4. Model description sample sequentially through 3 cartridges with diameter of 0.075 m and height of 0.5 m. The first filter was A 3-dimensional dispersion model coupled with a 0.45 mm polypropylene cartridge used to remove a hydrodynamic model was developed in this study. suspended solids. The second and third cartridges were The hydrodynamic model provided the physical param- made of Mn-fiber and used to absorb dissolved Ra eters (tidal elevation, current and eddy diffusion co- isotopes. The Mn-fiber was polyamide-fiber boiled in efficients), to drive the PDCM transport process in the dispersion model (Fig. 1). KMnO4 solution and prepared according to the method described by Xie et al. (1994). After sampling, the second and third cartridges were sealed in an air-tight 4.1. Hydrodynamic model plastic bag. The collection efficiency 3e was estimated as: The Princeton Ocean Model (POM, Blumberg and AC 3e ¼ 1 ð3Þ Mellor, 1987) was used to simulate the JZB tidal A B motions. The principal attributes of POM are as follows: where AB and AC are the activities of Ra isotopes in the (1) vertical mixing is calculated by a second-order second and third cartridges, respectively. Collection turbulence closure scheme (Mellor and Yamada, efficiency of 3e ¼ 0:3 G 0:03 was achieved in this study. 1982); (2) in vertical direction, a sigma coordinate is In laboratory, Ra isotopes were measured by using employed; (3) ‘Arakawa C’ grids in Cartesian coor- a Model GC3020 Canberra HPGe g-ray Detector with dinates are used in the horizontal plane; (4) the energy range of 4 keVe10 MeV. The resolution and horizontal differencing scheme is explicit; whereas the relative efficiency for 60Co 1332 keV emission were vertical one is implicit, thereby eliminating the time step 1.91 keV and 37.3%, respectively. The system’s in- constraints for the vertical coordinate and permitting tegrated background counts were 1.9 s1 at the energy the use of fine vertical resolution in the surface and range of 10e1635 keV. bottom layers; (5) the model has a free surface and split In the 228Ra measurement, all statistical errors of peak time steps; (6) complete thermodynamics have been areas of interest were less than 10%. The accumulated included (although they were not applied to the JZB error was less than 14%. The spectrum data acquisition waterbody). time was no more than 48 h. Since the g-ray branch In this study, POM was driven by four tidal compo- 228 ratio of Ra was too small to be used to measure the nents (M2,S2,O1 and K1) at the open boundary (OB2 in contents in environmental samples, in this study the Fig. 4). Due to weak stratification and small rate of river activity of 228Ra was measured with the g-rays of its discharge into JZB, only the barotropic process was daughters, and evaluated with the peak data at considered. With a horizontal resolution of 0.3#, there 338.7 keV (11.9%), 911.2 keV (27%) and 968.8 keV were 110 ! 80 grids in the study area (Fig. 4a). The 11 (16.3%) of 228Ac. s-levels provided average vertical resolution of less The specific activities of 228Ra in seawater were than 1.0 m in the bay area. The time steps for the inter- estimated, using the following equation (Liu et al., nal and external modes were 3.6 and 180 s, respectively. 2000): At the open boundary, a radiation condition was used 1 X3 1 N N for the normal component, with the tangential compo- A ð228RaÞ¼ si bi ð4Þ r 3L3 3 Y T T nent set to zero. For simplicity, the tidal flat (Fig. 2) was e i¼1 i i s b not included in the computational domain. Correspond- 3 228 where Ar (Bq m ) is the specific activity of Ra ingly, the normal velocity vanished at the outer edge of in seawater, L the volume of the seawater samples (m3), the tidal flat. 中国科技论文在线 http://www.paper.edu.cn

30 Z. Liu et al. / Estuarine, Coastal and Shelf Science 61 (2004) 25e35

N N 36.20° a 36.20° b

36.15° 36.15°

Open Boundary (OB1) Open Boundary (OB1) Open Boundary (OB2) 36.10° 36.10° ICT=1 Open Boundary (OB2)

T T 36.05° 36.05° OB1 OB1 36.00° XJ 36.00° XJ ICT=0

35.95° 35.95° OB2 OB2

120.15° 120.20° 120.25° 120.30° 120.35° 120.40° 120.45° 120.50° E 120.15° 120.20° 120.25° 120.30° 120.35° 120.40° 120.45° 120.50° E

Fig. 4. Horizontal grids with open boundaries (a) and initial concentration of the passive tracer for the numerical experiment (b). In the computational domain, there are totally 110!80 grids, of which only wet grids are plotted. ICT is the initial concentration ﬁeld.

4.2. Dispersion model the whole computational domain, whereas the amount of PDCM inside JZB may increase when tracers are In this study, a 3-D concentration transport model is carried back by currents. The long-term trend of tracer coupled to POM: concentration is, however, downward. After the tidal elevation reaches equilibrium in the vCD vCUD vCVD vCu v K vC C C C ¼ H CF ð6Þ hydrodynamic model, passive tracers are released in the vt vx vy vs vs D vs computational domain with the initial fields of 1.0 inside where C is the concentration of the passive tracer, U and and 0.0 outside JZB (Fig. 4b). Hence, the variation of C V are the horizontal and velocity components, re- represents the water renewal process in which YS water spectively, u is the vertical velocity (normal to the s progressively replaces JZB water. e surface), DhHðx; yÞChðx; y; tÞ, is the bottom topog- The dispersion model is solved with the Euler Lagrangian Method. For the advection process, the raphy and hðx; y; tÞ is the surface elevation, KH is the vertical eddy diffusion coefficient, and F is the horizontal previous positions of the particles are first calculated diffusion term: at each grid and then a linear interpolation is used to determine the concentration in the previous time step. v vC v vC The horizontal diffusion is calculated by an explicit F h DA C DA ð7Þ vx H vx vy H vy difference scheme, the vertical diffusion by an implicit difference scheme, resulting in each wet grid having where AH is the horizontal eddy diffusion coefficient. a linear equations group with coefficients of unknown The boundary condition along the coast is: variables in a tri-diagonal matrix. By solving these vC equations, the concentration fields at the next time step ¼ 0 ð8Þ v!n are obtained. There is confusion in the various studies related to the ! where n is the unit vector normal to the coast. timescales of water exchange (Bolin and Rohde, 1973; A commonly accepted assumption is that tracers are Prandle, 1984; Luff and Pohlmann, 1996). For example, absorbed completely at the open boundaries (Mooers different concepts are described by the same name, and Wang, 1998). In this study, however, the compu- whereas the same concept is described by different tational domain is extended outward about 10 km names (Takeoka, 1984). In light of recent relevant southward of the JZB channel and 16 km eastward publications, the average residence time (q)(Takeoka, from the JZB channel. Thus, there are 2 open 1984) was adopted as the water renewal timescale in this boundaries (OB1 and OB2 in Fig. 4) that serve as the study. outlets for PDCM. The boundary OB1 is at the channel Let t0 denote the initial time, t the time afterward between Xuejiadao and Tuandao, where PDCM is (t t0 > 0), and C(t) the tracer concentration. The allowed to re-circulate back to JZB, carried by tidal corresponding average residence time q of the tracer is: currents. The other boundary OB2 is on the southern

and eastern sides, where tracers are completely ab- Z N sorbed, thus their concentration is set to zero. The total q ¼ rðtÞ dt ð9Þ amount of PDCM actually decreases monotonically in 0 中国科技论文在线 http://www.paper.edu.cn

Z. Liu et al. / Estuarine, Coastal and Shelf Science 61 (2004) 25e35 31 where r(t)isC(t)/C(t0). The average residence time, q, 5. Results and discussion can be used to describe different water exchange pat- terns. The flushing time used by Bolin and Rohde (1973) 5.1. Simulation of tidal motions (the half-life time by Luff and Pohlmann, 1996) can be adopted as the timescale of the water exchange with a The simulation results indicated that stationary wave linearly (exponentially) decaying character. For the case features control the propagation of the tidally-driven of a linear pattern, r(t) can be defined as: system. Tidal currents in most areas flow back and forth. The modelled coamplitude and cophase of the M2 rðtÞ¼100% kt ð0%t%k1; k > 0Þð10Þ component indicated that tidal currents turn clockwise as they propagate in JZB, with maximal phase and amplitude difference of 3.5( and 0.07 m, respectively where k is the time rate of linear decrease. Thus, r(t) (Fig. 5a). The pair of strong clockwise residual eddies in equals to zero when t > k1. Based on Eq. (9), the 1 Fig. 5b is due to the geographic effect associated with results of q ¼ð2kÞ and rðqÞ¼50% can be obtained. Tuandao and Huangdao, and the north coast of Clearly, q represents the time required for the tracer Huangdao. This phenomenon was previously identified concentration to decrease to half of the initial value, through data analysis of residual currents (Editorial while flushing time is defined as the time required for Board of Annals of Bays in China, 1993). The synoptic a given tracer to vanish. Hence, q in this study equals to distributions of simulated currents over a full tidal cycle half of the flushing time. In the exponentially decaying show that YS water enters JZB at maximal speed of pattern, r(t) is given as: about 0.75 m s1 at the channel and leaves JZB at about 0.85 m s1. The structure of tidal currents and tidal rðtÞ¼elt ðl > 0Þð11Þ residual currents simulated in this study is consistent with that in previous works (e.g., Chen et al., 1999). Since there where l is the exponential decay coefficient. Under such is no water flux across the tidal flat, the simulated current circumstance, the results of q ¼ l1 and rðqÞ¼e1 are near the edge of the flat might actually be smaller. calculated. Since the half-life time is defined as the time Fig. 3a shows that the model outputs of JZB tidal needed for the radioactivity to decrease to 50%, q is elevation from September 9 to October 8 (1993) agreed about 1.44 P ¼ðln 2Þ1R times the half-life time in the case well with observations at the Dagang tide station of exponential decay. Eqs (9), (10) and (11) are useful for (Fig. 2), so the model can be used to simulate the spring converting flushing time and half-life time into their and neap tides. corresponding average residence time. It is helpful for the Fig. 3b compares the observed and simulated drift discussion on the comparison of the results in this study trajectories in Z1, Z2 and Z3. The maximal difference is with previous results (Section 5.4). less than 1.0 km for Z3. The modelled trend of tidal

N N Cophase ( deg., local ) a b 36.20° Coamplitude ( m ) 36.20°

36.15° 36.15°

DG DG 36.10° 36.10°

H T H 36.05° 36.05° T

0.15 m/s

XJ XJ 36.00° 36.00°

120.168° 120.218° 120.268° 120.318° E 120.168° 120.218° 120.268° 120.318° E

Fig. 5. Computed cophase (deg. local) and coamplitude (m) (a); tidal residual current ﬁeld (b) of the semidiurnal tidal constituent M2 in JZB. 中国科技论文在线 http://www.paper.edu.cn

32 Z. Liu et al. / Estuarine, Coastal and Shelf Science 61 (2004) 25e35

Table 1 was not measured, sb in Eq. (1) is assumed to be the Salinity in JZB during three cruises conducted in August 2001 mean summer salinity in the 1990s (i.e., 30.99 given by Date Mean Range Root mean Yang and Wu, 1999). Thus, the initial rain fraction f(t0) (mm/dd/yy) (sampling number) square was about 6.55% as calculated by using Eq. (1). After 8 08/13/01 28.96 (n ¼ 22) 25.35e29.43 1.56 days, salinity in the bay reached 29.7 (increasing by 08/21/01 29.73 (n ¼ 22) 26.99e30.20 1.23 0.77), indicating that the remnant water index [i.e., P in e 1 08/28/01 29.93 (n ¼ 22) 28.53 30.37 0.53 Fig. 6a] was 62.1% according to Eq. (2). In other words, 37.9% of the original water was renewed through ex- velocity rotation is consistent with that of Z1. After 9 h, change with the YS water, with an average daily recovery Z2 was discontinued due to local strong wind. Although rate of about 5.42%. The recovery process was, however, the net excursion for Z2 was successfully simulated, slowed down in the next week. On August 28, salinity there was obvious difference between the simulated and increased to 29.9, indicating that the remnant water still observed drifter trajectories. Aside from the limitations contributed 52.2% [i.e., P2 in Fig. 6a] of the bay water of the model, the difference was in part due to the non- and that the average daily exchange rate was 1.41%, only linear interaction between the oscillating tidal currents about 1/4 of that measured in the first 8 days. and the double residual eddies (Zimmerman, 1986). Table 2 shows the specific activity of 228Ra and the Although the initial positions of the two particles were estimated water exchange rate at Stations B3 and C2. identical, the separation between their trajectories could The exchange rate varied greatly from station to station grow exponentially due to the ‘‘tidal random walk’’ in JZB; so JZB should not be taken as a single box with process. uniform concentration. Data in Table 2 also indicate that the exchange rate at B3 was faster than that at C2, 5.2. Salinity recovery and 228Ra measurements although C2 was closer than B3 to the bay channel. The modelled tidal exchange rate at B3 being also greater In summer, salinity in JZB is relatively lower than that than that at C2 (Table 2) accorded with the 228Ra in YS, resulting in salinity decreasing from the bay observations. channel to the northern part of JZB. The statistical parameters are shown in Table 1. Using the approach of 5.3. Average residence time Takeoka (1984), the entire JZB was taken as a continuum. The change in JZB’s mean salinity can be used as basis to After the tidal elevation reached equilibrium in the obtain the remnant water index in Eq. (2), so that the hydrodynamic model, the concentration at high tide was output by the dispersion model can be validated. initialized and the model was run for the next 200 days. The initial mean salinity [i.e., s(t0)] of JZB was 28.9 In order to determine the average condition of on August 13, 2001. Since salinity before the rainstorm JZB, the average concentration (AC) of PDCM was

N 100 a b Water Exchange Process 36.20° Simulation Observation 90

70 DG 36.10° %

H P0 = 100% T 50

P1 = 62.1% 40 XJ 36.00° P2 = 52.2%

30 0 5 10 15 20 25 30 120.15° 120.20° 120.25° 120.30° 120.35° E time (day)

Fig. 6. Results of simulation and observation of water exchange process (a) and distribution of average residence time (day) in JZB (b). Simulated water exchange process is plotted based on modelled concentration of passive tracers; the bar chart in (a) was obtained from the calculation of remnant water index (i.e., P in Eq. (2)), based on the observation of salinity recovery after the rainstorm. 中国科技论文在线 http://www.paper.edu.cn

Z. Liu et al. / Estuarine, Coastal and Shelf Science 61 (2004) 25e35 33

Table 2 slow down the water exchange process. The clockwise 228 Specific activities of Ra during a tidal period and tidal exchange rate (anti-clockwise) eddy between Tuandao and Huangdao at B3 and C2 stations (in the north of Huangdao) was favorable (unfavorable) Date Tidal Station 228Ra Tidal exchange rate (%) for the transport of PDCM from JZB to the YS, which (mm/dd/yy) phase (Bq m3) Observation Simulation resulted in dense isopleths of residence time westward. 08/21/01 Low B3 30.21 (G2.92) 23.2 (G9.2) 23.9 This phenomenon accorded with the output by parcel- 08/21/01 High B3 23.21 (G2.63) tracking method (Zhao et al., 2002). 08/23/01 Low C2 29.65 (G3.32) 0.9 (G8.0) 16.1 G 08/23/01 High C2 29.38 ( 2.39) 5.4. Comparison of our results with results of The locations of B3 and C2 are shown in Fig. 2. Measurements of previous studies 228Ra were conducted on one sample per station of interest. Experimental errors are given in parenthesis. In previous studies (Table 3), several methods were applied to study the water exchange. The timescales of examined. The results showed that AC was obviously water exchange were converted into average residence affected by the periodic tidal motion (Fig. 6a). During time, based on Eqs. (9), (10), and (11). Hence, it is ebb tide, the bay water carries PDCM to the YS, so the possible to compare the results of previous studies and high PDCM concentration water gradually dominates results of our study. Based on the simulated Lagrangian JZB, resulting in the increase of PDCM AC. During residual currents by a 2-dimensional ADI model, Sun flood tide, PDCM AC decreases in JZB and the et al. (1988) concluded that the water masses at the amplitude of AC is considerably high because JZB is northern part of JZB remain inactive; but that those in shallow and the tidal flux has a strong influence on the the bay center are active; and that those at the channel stability of the water volume. Along with the de- have the highest self-purification capability. Based on velopment of water exchange induced by tides in JZB, the analysis of salinity data, Wu et al. (1992) pointed out AC oscillates and slowly declines to zero. The average that the exchange rate between waters inside and outside residence time is about 52 days estimated by Eq. (9). JZB is about 7% per tidal cycle, and that the half-life The relationship between the residence time and the time predicted by the box model they used was about initial concentration was next examined in more detail. 5 days. The flushing time might be about 10 days accord- The model was run for passive tracers with different ing to results from another box model (SOA and QAB, initial concentrations of 100, 50, 30, 10 and 5, 1998). Zhao et al. (2002) modelled the trajectories of respectively, and the results showed that the residence water particles with various initial positions and pointed time of 52 days remained unchanged. Thus, the average out that due to the spatial variation of the tidal residual residence time in this study was independent of the current field, the mean residence time could vary from 7 initial concentration of the passive tracer. The average days to several months, at an average of about 80 days. residence time differed by only 5e10% if the initial The previous studies have some shortcomings. For pollutant-release time changed from the flood to ebb example, the model simulation by Sun et al. (1988) could tides, which suggested that the model was not sensitive not produce quantitative timescales of water exchange. to change in drainage time of pollutants in JZB. The exchange time in this study was significantly greater With regard to the spatial distribution of average than that yielded by the box models (Wu et al., 1992; residence time in JZB, the model outputs showed that SOA and QAB, 1998) based on the assumptions of average residence time between the surface and near uniform current field and instantaneous mixing. As the bottom waters was similar due to strong vertical tidal current field is not homogeneous in JZB, it should not mixing. The average residence time increased northward be treated as a single box with uniform conditions. So from the channel to the northern part of JZB and at the box models (Wu et al., 1992; SOA and QAB, 1998) may western side was longer than that at the eastern side. The overestimate the water exchange capability of JZB. average residence time near the channel was less than Our study and that of Zhao et al. (2002) yielded quite 10 days, but in the western part of the bay was more similar tidal current fields. In addition, similar defini- than 100 days (Fig. 6b). This phenomenon closely tions (‘‘mean residence time’’ and ‘‘average residence related to the geomorphology and structure of the tidal time’’) are used to characterize the water exchange residual currents. The channel between Tuandao and timescale in JZB. There are, however, three main Xuejiadao was the only passage for water exchange differences. First, in the parcel-tracking model of Zhao between JZB and the YS; so the southern JZB water was et al. (2002) the diffusion process is neglected, resulting first replaced by the inflow of YS water during flood in underestimation of water exchange capability in time, resulting in the pattern of average residence time in coastal region where diffusion dominates. Second, the JZB (Fig. 6b). The direction of tidal residual currents mean residence time in Zhao et al. (2002) was defined as (Fig. 5b) in the western part of JZB was mostly the time needed for the concentration of the passive northward, and so tended to pile up PDCM there and tracer in a given region to decay to e1 (37%) of the 中国科技论文在线 http://www.paper.edu.cn

34 Z. Liu et al. / Estuarine, Coastal and Shelf Science 61 (2004) 25e35

Table 3 Comparison of results on the water exchange in Jiaozhou Bay Authors Model Features Conclusions Sun et al. (1988) 2-D ADI 1. Tidal Lagrangian residual current field is plotted, Water parcels near the bay channel is most based on the model simulation. active; those around the coast are inactive; the central part of the bay is characterized by moderate water exchange capability. Wu et al. (1990) 0-D Box 1. Tidal flux and water exchange rate are obtained The half-life time is about 5 days, and the from field observations. corresponding average residence time is 2. Water exchange process is described in terms of a about 7.2 days. linear function of time. 3. The bay is assumed to have uniform concentration of PDCM. SOA and QAB 0-D Box 1. Tidal flux is calculated by a numerical model. The flushing time is about 10 days, and the (1998) 2. Water exchange process is described in terms of a corresponding average residence time is linear function of time. about 5 days. 3. The bay is assumed to have uniform concentration of PDCM. Zhao et al. 3-D 1. The hydrodynamic model is calibrated by The mean residence time is about 80 days. (2002) Parcel-tracking drift experiments. 2. The diffusion process is neglected. 3. The water exchange process is described in terms of an exponentially decaying function of time. This study 3-D Dispersion 1. More complete physical processes The average residence time is 52 days. (i.e., advection and diffusion) are included. 2. Both the hydrodynamic and dispersion models are supported by field observations.

initial value. Accordingly, these two approaches yield the important physical processes of water exchange are the same results only if the water exchange curve is included in the model. Second, the interdisciplinary exactly exponentially decaying. The water exchange, approaches, including salinity recovery and radioisotope however, does not fit the exponentially decaying curve. measurements, are integrated and provide crosschecks Finally, in the parcel-tracking model in sigma coor- for the results from the dispersion model. dinates, each passive tracer represents a different water The computational domain in this study, however, volume. Consequently, the tracers should be given did not include the JZB tidal flat. So the model may different weights. For example, the parcel initially in underestimate the water exchange capability of JZB. deep region gives more important contribution than that Water exchange processes could be also influenced by in shallow region, but this was not taken into account in other processes, such as winds in winter. These questions the study of Zhao et al. (2002). are left for further study.

6. Conclusions Acknowledgements The average residence time of JZB water is about 52 days, as calculated by a 3-dimensional dispersion model. This research was conducted as a component of the The modelled curve of water exchange accorded with project ‘‘Watersheds Nutrient Loss and Eutrophication the salinity recovery process after a rainstorm. Both our of Jiaozhou Bay’’ funded by National Natural Science model output and intensive measurements of the 228Ra Foundation of China under grant 40036010. We thank specific activities in JZB showed significant differences in Dr. Eric Wolanski, editor of ECSS, and two anonymous the water exchange rate at the stations of interest. The reviewers for their valuable comments and suggestions. spatial distribution of the average residence time is We are grateful to Prof. Rui Xin Huang of Woods Hole nearly insensitive to the drainage time and is mainly Oceanographic Institution, Prof. Shengchang Wen and determined by two factors: the tidal residual current Prof. Jingyong Wang of Ocean University of China for field and the distance to the bay channel that is the only their suggestions and encouragement. We are obliged to passage connecting JZB to the YS. Comparison of Dr. Roger Z. Yu, English editor of the English language different approaches applied to JZB showed that the Chinese Journal of Oceanology and Limnology, for his method in this study has two unique features. First, all kind help. 中国科技论文在线 http://www.paper.edu.cn

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