A high-resolution, three-dimensional, POM-based numerical model is developed to study the distributional responses of sunken algae (SA) in a massive macroalgal bloom, which occurred in Qingdao coastal waters in summer 2008, to the barotropic tidal currents which dominate the dynamic circulation system. Validated by in situ observation of both sea level and buoy-measured current data, the model shows satisfactory performance in reproducing the tidal system. An indicator BotDIV, the integral of velocity divergence of bottom flow over hours preceding the trawling of SA, is diagnosed on the basis of tidal modeling. It is found that the distribution of SA, captured by 16 tows of bottom trawling, is dependent on the BotDIV field. Basically, large (small) quantity of algae are caught at the sites where bottom currents converge (diverge). The influences of advective or diffusive process on the distribution of such heavy seaweeds settling on the seabed are probably limited.
 Between late May and July 2008, public attention was drawn to a sudden outburst of a giant macroalgal bloom occurring in the coastal waters of Qingdao (also known as Tsingtao), China, the host city of the Sailing Regatta of the 29th Olympic Games (Figure 1). Such massive accumulation of macroalgae, often descriptively termed “green tides”, is by no means novel to the world: it has been increasingly widespread globally for decades as a result of marine eutrophication, occurring usually in estuaries and shallow embayments [Morand and Merceron, 2004]. Morand and Briand  had listed 37 countries or American states which had suffered from green tides. This macroalgal bloom in Qingdao is caused by the explosive proliferation of Enteromorpha. Hayden et al.  suggested that Enteromorpha and Ulva should belong to the same genus, Ulva. However, they are traditionally regarded as different species for their dramatic differences in gross morphology. Such green algae are generally believed to be non-toxic, but their excessive growth still results in negative consequences including environmental effects such as anoxia from the rotting seaweeds in the water, and socioeconomic problems from spoiling the amenity of beaches by the decomposition of stranded seaweeds, especially in tourism spots. These problems have been illustrated in the Venice Lagoon, Italy and Brittany coasts, France [Morand and Merceron, 2004]. As for Qingdao, the most urgent task was to remove the algae to avoid potential anoxia and pollution, and ensure a smooth Sailing Regatta.
 First found about 140 km away from the land at the end of May, the floating algae began to invade Qingdao coasts around 15 June. It was reported by aerial surveillance that massive algae aggregated in the waters of Olympic Regatta Venue (ORV) on 22 June, and reached its peak around 28 June, when about 30% of the total area of ORV was covered by green carpets. The development of this green tide is shown in the daily satellite images captured by Moderate Resolution Imaging Spectroradiometer (MODIS) onboard NASA's Aqua and Terra satellites (Figure 1). In late June, the thickness of algae mats stranding on the beach was about 30 cm, and peaked over 100 cm at Zhanqiao Pier. About 1200 boats and more than 20,000 people were involved into the heroic cleanup efforts, and a total of 752,000 tons of algae were mechanically removed by 14 July 2008.
 During the cleanup of drifting seaweeds, many algae were found sunk to deep water and became invisible to naked eye. This made the mechanical removal of algae very difficult. This paper is intended to study the dynamical influences of tidal circulation on the distribution of sunken algae (SA) by numerical modeling.
2. Data and Methodology
2.1. Study Area
 Qingdao lies in the southeast part of Shandong peninsula facing the Yellow Sea (YS). Most water in the study area is shallower than 30 m, except a deep channel lying across the mouth of Jiaozhou Bay (Figure 2). Along this trench, strong tidal currents flux into and out of Jiaozhou Bay at a peak speed exceeding 150 cm s−1 during spring tides [Lü et al., 2008]. Tidal flow is the most dominant movement in the circulation system in YS. A bottom-mooring observation by an Acoustic Doppler Profiler deployed at (120.9°E, 35.0°N) revealed that the summer residual current was only 4 cm s−1 [Liu et al., 2008], about one order smaller than tidal current. Previous studies using drifter tracking observation [Beardsley et al., 1992], satellite data [Yanagi et al., 1997], and numerical modeling [e.g., Xia et al., 2006] all suggested that the speed of YS summer circulation is only in the order of 100–101 cm s−1.
2.2. Buoy Data
 Five SEAWATCH WAVESCAN buoys, produced by Fugro OCEANOR, were deployed in ORV to provide information for the Olympic Sailing Regatta (Figure 2b). The buoys collect multiple environmental data such as current speed and direction, wave height and direction, sea surface temperature, and meteorological parameters. The measurement accuracy of current speed, current direction, and sea temperature is 1 cm s−1 (or 2% of reading), ±2.5°, and ±0.03°C, respectively. The real-time data are transmitted by satellite communication system to data processing center, and distributed operationally to the world via internet. We use the current data from the buoys and water level observation from Xiaomaidao station to calibrate and verify the numerical model. The tidal level at Xiaomaidao and current data of Buoy A are provided hourly, while the sampling interval for other buoys is 10 minutes.
2.3. Bottom Trawl Catches of Algae
 Bottom trawl is a mobile fishing gear consisting of large nets which are dragged across the seafloor to catch groundfish and other species. During 4–12 July, bottom trawl cruises were carried out by fishing vessel (F/V) Lujiaoyu 0091, Lujiaoyu 0092, and Luqingyu 0168 to catch the sunken algae, and a total of 16 tows was completed (Figure 2b). The cruises are divided into two groups according to trawling method: Group A (single-boat trawling by F/V Luqingyu 0168), and Group B (double-boat trawling by F/VLujiaoyu 0091 and Lujiaoyu 0092). The trawl net used in Group A is 2 m high and 20 m wide, while the net of the double-boat can stretch 10 m in height and spread over 35 m wide. The SA captured in each tow was weighed for fresh weight.
2.4. Numerical Modeling
 A barotropic tidal model based on Princeton Ocean Model (POM) [Blumberg and Mellor, 1987] is developed to numerically predict the currents. The model covers an area of 120.075°E–120.575°E, 35.938°N–36.266°N, as shown in Figure 2a, with a fine horizontal resolution of 0.12′ × 0.12′ (∼180 m × 220 m) and evenly spaced six sigma layers in the vertical. A wetting and drying scheme is designed to handle the movable land-sea boundaries in Jiaozhou Bay [Oey, 2006; Oey et al., 2007], where extensive mudflats are regularly exposed from shallow waters (Figure 2a).
 Numerous Darwin's harmonic constituents can be combined into four principal constituents M2, S2, K1, and O1 in tidal prediction [Doodson and Warburg, 1941]. Similarly, Fang  proposed an improved “quasi-harmonic constituent method” which took shallow-water constituents into consideration with higher accuracy. Following Fang , the model is forced at the open boundary by tidal height
where i ranges from 1 to 6, representing the quasi-harmonic constituents M2, S2, K1, O1, M4, and MS4, respectively. H is tidal amplitude, g is phase lag, D is amplitude coefficient, d is epoch correction, and ω is the frequency after adjustment. The boundary values of H and g are obtained by interpolation from a tidal model which covers East China Sea and the Southern YS [Lü et al., 2007]. The formula computing D, d, and ω is given by Fang .
 Initialized from a state of rest, an initial spin-up period of 30 days is used to suppress transients, and the subsequent 30 days are then analyzed using the least squares error method to get the harmonic constants.
3. Results and Discussion
3.1. Model Validation
 The main tidal features in the study area are reproduced by the model. The co-tidal charts and tidal energy flux vectors (figure not shown) reveal that the tidal waves come from the east and propagate southwestward, and are clearly dominated by M2 constituent whose height amplitude at Buoy A is roughly 4.5 times larger than that of K1 tide.
 The model performance is validated by comparisons between observation and modeling. A point by point comparison of totally 186 hourly measurements at Xiaomaidao (Figure 3a) shows that the mean absolute error of tidal level prediction is 8.9 cm, which is acceptable against the background of high tidal range (about 4 m in spring tide). The observed and modeled time series of tidal currents at three buoys are plotted in Figures 3b–3e. At these buoys, both phase and amplitude of the predicted current are consistent with observations to a satisfying extent. The velocity modeling accuracy is given quantitatively at Buoy A in two ways. First, harmonic analysis of an observed 44-day time series of u and v components is performed to derive the harmonic constants of principal tides. The obtained amplitude and phase-lag (referred to 120°E) of M2 tidal current are 72.5 cm s−1 and 279.7°, respectively, for u, and 27.5 cm s−1 and 264.4°, respectively, for v, showing good agreements with model results: 72.1 cm and 278.8° for u; 29.5 cm s−1 and 263.0° for v. Second, the mean absolute errors of current direction and speed are computed as 8.0° and 10.5 cm s−1, respectively, counting in all the available data except the points when slack current occurs. The good performance of the model justifies its further application in studying the effects of tidal flow in distributing sunken algae.
3.2. Distributions of Sunken Algae
 Few studies can be found discussing the distribution of SA in macroalgal bloom events. It seems natural to suppose that the sunken seaweeds may flow with currents, but as demonstrated below, the bottom velocity divergence, BotDIV ≡ ∇ • Ub where Ub is the two-dimensional tidal current vector near bottom, is found to be the key factor determining the horizontal distribution of SA.
 The instantaneous BotDIV field can be easily diagnosed once Ub is produced by the model. As the tidal height, BotDIV changes smoothly with the tidal cycle. Here we calculate BotDIV as the integral mean of ∇ • Ub over three hours before the mean time of trawling and along the trawling track. The bottom trawling captures of SA of the total 16 hauls, together with the corresponding BotDIV, are presented in Figure 4, which shows a pretty clear relationship between the algae catches and BotDIV field. Note that the bottom flow is convergent (divergent) if BotDIV is negative (positive). Basically, in the waters where bottom currents are divergent few algae are captured, except Tow A3 in which 12.25 kg algae is caught per 100 m; the catches of the other tows range from 0.02 (B4) to merely 0.71 kg/100 m (A4). On the contrary, four out of the six tows accompanied by strong convergence harvest the highest values of sunken algae which amount to nearly 30 kg/100 m during Tow A1 and A5–A7. As for Tow A11, B1, and B2, the convergence of Ub is almost zero, which is not contradictory to the corresponding small catch weight of SA. Figures 4b and 4c provide two snapshots of BotDIV field, illustrating its influences on the aggregation of sunken algae.
 The seeming “exceptional” tows of A8, A9, and A2 can be understood as results from multiple reasons. Very few SA were caught during Tow A8 on a convergent background. First, the Ub near A8 had just experienced a long period of divergence for seven hours before trawling, so few SA had been reserved there when operation began. In addition, the trawling was conducted during slack tide period when the weak current was changing direction, thus the influence of advection was almost negligible. Tow A9 captured a large amount of SA of 300 kg in a 645 m cruise when BotDIV is neutral. The upstream convergence of Ub was obvious, so the advection effects might account for the piling of SA. Only 13.6 kg of SA was caught in 368 m during Tow A2 despite the convergent field. Lack of algae in the surrounding waters is a possible reason. Besides, a large area of intense divergence was found upstream to A2 site, implying that advective process could not help accumulate SA.
 In general, the transport of soluble materials or very fine articles, such as some pollutants, nutrients, or suspended sediments in the ocean, is highly dependent on the processes of advection and diffusion of sea water, and their distribution can even be figured out by solving the differential equations similar to those of temperature and salinity under conditions. But the sunken macroalgae are different from the soluble materials. In this macroalgal bloom in Qingdao, the long, filamentous branches of Enteromorpha usually tangle each other tightly, forming strong concentrations. The algae mat in Brittany was even found in depths of 20 cm and 40 m across in water [Morand and Merceron, 2004]. Given that the large body of algal mats has settled on the seafloor, very strong external impulsion is needed to overcome bottom friction and force it to refloat unless oxygen is produced to fill the inner tubes of Enteromorpha again. Such heavy SA is very likely not much susceptible to advective or diffusive processes, and the BotDIV field should be the most important factor controlling the rapid distribution of SA.
 A severe macroalgal bloom broke out in Qingdao coastal waters between late May and July 2008, and great efforts were made to eradicate the seaweeds. However, the cleaning job became difficult when the algae settled to the seabed and became invisible to naked eye. This paper seeks to investigate the linkages between tidal dynamics and the horizontal distribution of sunken algae by using a prognostic, three-dimensional, barotropic tidal model based on POM, and aims at facilitating the algae cleaning task.
 We first focus on modeling the major tidal constituents (M2, S2, K1, O1, M4, and MS4) to acquire a precise prediction of tidal currents. Satisfactory agreements are obtained between numerical simulation and in situ observation of both sea level and current data. Attention is then paid to the association of SA captures from bottom trawling with the divergence field of the bottom current velocity. The distribution of sunken algae catches seem closely related to the integral of divergence field over hours preceding trawling: the algae are prone to congregate at the sites where bottom current constantly converges; in the waters characterized by strong divergence, only small amount of algae can be caught. Other processes such as advection may also contribute to the distribution of SA, but their influences are probably subsidiary in comparison with the divergence field.
 This study was supported by the National Natural Science Foundation of China (grant 40806016) and National Key Technology R&D Program (grant 2008BAC49B02). We thank Yonggang Wang for his help in harmonic analysis of tidal current at Buoy A. Satellite images courtesy of MODIS Rapid Response Project at NASA/GSFC. The buoy observation data were freely downloaded from Beijing 2008 Olympic and Paralympic Sailing Weather Service website: http://www.nmfc.gov.cn/english/afszq.aspx, maintained by Qingdao Municipal Bureau of Ocean and Fisheries, and North China Sea Branch of SOA.