A nitrogen-based four-compartment ecosystem model coupled with a physical model is applied to the Japan Sea. Seasonal variability in ecosystem dynamics simulated by the coupled model is in good agreement with the observations. A set of artificial tracers labeled according to specified regions is introduced to identify nutrient sources in the surface layer of the Japan Sea. The results of the labeled tracer experiment show that one of the large nutrient sources in the southern Japan Sea is located along the east coast of Korea. The upward flux of dissolved inorganic nitrogen along the east coast of Korea and the nitrogen flux through the western channel of the Tsushima/Korea Straits (TKS) sustain high primary productivity in the southwestern Japan Sea. The surface nutrient conditions in the nearshore region along the Japanese coast depend on the nitrogen flux through the eastern channel of the TKS throughout the year. Since materials transported through the TKS have significant impact on the biological productivity of the southern Japan Sea, field observations of chemical and biological data, in addition to physical ones, should be continued in the TKS.
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 The Japan Sea is a semi-enclosed marginal sea located in the northwest Pacific (Figure 1). The Japan Sea is called a “miniature ocean” because the western boundary current flows along the Korean coast, the cold bottom water is generated in the northern part during the winter and its dynamic characteristics are nearly the same as those of a global ocean [Ichye, 1984].
 The Tsushima Warm Current (TWC) horizontally supplies heat, water, and materials through the Tsushima/Korea Straits (TKS) to the Japan Sea, affecting the hydrographic conditions and ecosystem dynamics in the Japan Sea. Recently, temporal and spatial variations in phytoplankton pigment have been revealed by ocean color images of the Japan Sea [Kim et al., 2000; Yamada et al., 2004]. Two phytoplankton blooms can be seen in spring and autumn, suggesting that hydrographic conditions, which include mixed layer depth (MLD), are important factors impacting temporal and spatial variations in phytoplankton. Onitsuka and Yanagi  constructed two ecosystem models, applying climatological MLD and euphotic layer depth data, to investigate the relationship between hydrographic conditions (for example, water temperature, MLD) and ecosystem dynamics in the Japan Sea. They demonstrated that the differences in ecosystem dynamics between the northern and southern parts of the Japan Sea are primarily caused by differences in hydrographic conditions under which the Tsushima warm water either exists or not. The results suggest the indirect influence of heat and fresh water supplied by the TWC on the ecosystem dynamics in the Japan Sea.
Morimoto et al.  conducted three field observations from the TKS to the region off the San-in coast, on the western part of Honshu, Japan, in early winter in 2001, 2002, and 2004. They showed that the high-observed chlorophyll a (chl.a) concentration corresponds to the strong geostrophic current region, especially in the second branch of the TWC. The results imply the direct influence of materials transported horizontally by the TWC on the ecosystem dynamics in the Japan Sea.
 Furthermore, nutrients supplied by the coastal upwelling should be considered in an assessment of the southwestern part of the Japan Sea. The cold water mass frequently appears at the sea surface along the southeastern coast of Korea in summer [Seung, 1974; Lee, 1983; Byun and Seung, 1984; Lee and Na, 1985; Byun, 1989]. The intensity of currents, southerly wind, and bottom topography were proposed to contribute to the frequent localization of surface cold water along the southeastern coast of Korea [Byun and Seung, 1984; Lee and Na, 1985]. The existence of localized surface cold water has been confirmed by satellite sea surface temperature and ocean color images, which show increased chl.a concentration along the Korean coast (Kang et al., Upwelling along the southeastern coast of Korea, submitted to Continental Shelf Research, 2007).
 The above results suggest that nutrients directly supplied by the TWC and upwelling along the east coast of Korea, as well as by the development of MLD in winter, contribute to the biological productivity in the Japan Sea. However, there have not been any studies that reveal their influences on the ecosystem dynamics in the Japan Sea. The present study applies a nitrogen-based three-dimensional ecosystem model coupled with a physical model to the Japan Sea. First, we show temporal and spatial variations in the ecosystem dynamics. Second, we carry out a labeled tracer experiment to identify nutrient sources in the surface layer of the Japan Sea. We particularly focus on the roles of the TWC and upwelling along the east coast of Korea as nutrient sources.
2. Model Description
2.1. Physical Model
 The Japan Sea version of the Research Institute for Applied Mechanics, Kyushu University (RIAM) Ocean Model developed by Lee et al.  is used as the physical model for this study. The RIAM Ocean Model is a free surface primitive ocean general circulation model. This model assumes a hydrostatic balance using the Boussinesq approximation and solves the three-dimensional, nonlinear, primitive external and internal mode equations on the Arakawa B-grid system [Lee et al., 2003]. The grid spacing is 1/6° in the zonal and meridional directions. There are 46 levels, with thicknesses ranging from 5 to 600 m in the vertical direction. The vertical level range is fine near the surface layer (i.e., 5 m for the upper 50 m; 10 m from 50 to 150 m). The bottom and coastal topographies are given by a combination of the ETOPO5 (5-min Earth Topography) depth data from the National Geophysical Data Center. The topographies are adjusted in the TKS to maintain the volume transport ratios through the western and eastern channels, specifically, the Tsushima Islands are shifted one grid to the south. This modification has a negligible effect on the physical fields in the Japan Sea.
 Parameters used in the physical model are based on those of Lee et al. , with the exception of the vertical eddy viscosity and diffusivity coefficients. The vertical eddy viscosity and diffusivity coefficients are calculated in the mixed layer model. The mixed layer model used in this study is a second-order turbulence closure model developed by Noh and Kim . The model is driven by the surface and horizontal fluxes. The surface wind stress, net heat, and water fluxes are given by the climatological monthly mean values processed from the daily forecast of the European Center for Medium-Range Weather Forecast during November 1992 to October 2000.
 The vertical profile of solar radiation absorption is modeled using the analytical formula in Paulson and Simpson . In the present study, we have not attempted to model the feedback of phytoplankton concentration on the model physics owing to the absorption of solar radiation. The simulated temperature and salinity at the first level are restored to the monthly mean sea surface temperature and salinity linearly interpolated into daily data with a 30-day timescale. They are obtained from the Japan Oceanographic Data Center (JODC).
 The inflow conditions at the TKS are extrapolated from the long-term monthly data set on the basis of in situ temperature and salinity collected by the JODC and the Fisheries Research Development Agency of Korea and volume transport from the acoustic Doppler current profiler (ADCP) measurements with an annual average of 2.61 Sv (1 Sv = 106 m3 s–1) [Takikawa et al., 2005]. The volume transport has regular seasonal variation with double peaks in May and October.
 The outgoing volume transport through the Tsugaru Strait is fixed as 1.4 Sv from the ADCP measurements [Shikama, 1994]. The volume flowing out through the Soya Strait is then adjusted to maintain the mass balance within the domain. The volume transports are equally distributed to each grid along the open boundaries. The model is at rest initially and has climatological mean temperature and salinity distributions in January on the basis of the JODC data.
2.2. Ecosystem Model
Onitsuka and Yanagi  assumed that photosynthesis is limited by nitrogen availability throughout the year in the Japan Sea, because the ratio of nitrate to phosphate is less than the Redfield ratio (N:P = 16:1) [Redfield et al., 1963] and silicate is sufficient compared to nitrate throughout the year. They compared the results of two ecosystem models differing in ecological complexity, a four-compartment nutrients, phytoplankton, zooplankton, and detritus (NPZD) model and a nine-compartment model that includes two categories of phytoplankton and three categories of zooplankton. Seasonal variations in several parameters (for example, chl.a, nitrate, primary production) are not significantly different between the two models. The study indicated that with careful selection of biological parameter values, the NPZD model could calculate such parameters in the Japan Sea. Therefore the ecosystem model used in the present study is a nitrogen-based four-compartment NPZD model (dissolved inorganic nitrogen, DIN; phytoplankton, PHY; zooplankton, ZOO; detritus, DET), as described in Figure 2. The state variables obey the following equations,
where C is the state variable in the ecosystem model; t is the time; λ is the longitude; ϕ is the latitude; and R is the radius of the earth. L and ∇2denote advection and Laplacian operators, respectively. Kh and Kv represent the horizontal and vertical eddy diffusivities, respectively. B(C) is the biochemical term of each compartment (see Appendix), based on that originally developed by Kawamiya et al. . The parameters used in the ecosystem model are almost the same as those in the work of Onitsuka and Yanagi  (Table 1).
 Monthly mean boundary conditions of DIN and PHY at the TKS are given by the nitrate and chl.a data from the World Ocean Database 1998 (WOD98) [Conkright et al., 1998]. There are no data for ZOO and DET at the TKS. Both ZOO and DET at the TKS are set at half of the PHY concentration on the basis of the results obtained by Onitsuka and Yanagi , which showed that they were almost half of the PHY in the southern Japan Sea. Initial concentrations of PHY, ZOO, and DET are set at 0.1 mmolN m−3 in the model domain. Initial DIN concentration is given by the climatological mean value in winter, processed from the WOD98. Calculations are carried out in units of mmolN m−3. Chl.a concentration is estimated using C:chl.a ratio (50:1) and Redfield ratio (C:N = 106:16).
 Temporal integration is carried out for 12 years to spin the physical model up as is the case with Yanagi et al. . The circulation pattern in the upper layer (<200 m) visibly attains asymptotic steady state after integration for a period of 12 years but is not achieved in the deeper layer. The effect of less efficient reproduction in the deeper layer is not large because only the biochemical processes in the euphotic layer with a thickness of less than 100 m are considered. The coupled model has been subsequently integrated for 4 years. The results for the last year, when it is in quasi-steady state, are given below.
3. Physical and Biological Fields
 The distinct features of circulation in the surface layer of the Japan Sea, such as the western boundary current called the East Korean Warm Current flowing northward along the Korean coast, the first branch of the TWC flowing along the Japanese coast, the Liman Cold Current, and the Korean Cold Current flowing southwestward along the Russian and Korean coasts are reproduced in Figures 3a and 3d. There is a strong temperature front along 40°N (Figures 3b and 3e). We can see warm and cold areas in the water associated with meanders of the TWC and eddy activities. Salinity in the TWC has a significant seasonal variation (Figures 3c and 3f). In summer, fresh water, originating in the great rivers of China increases in the TWC [Isobe et al., 2002; Chang and Isobe, 2003]. Low salinity water enters along the TWC and extends into a broad area of the TWC region in the surface layer, remaining until autumn.
 The calculated monthly mean MLD in February is shown in Figure 4. The MLD develops a depth of more than 200 m in the broad area north of the subpolar front. In contrast, the MLD remains shallow (<100 m) south of the subpolar front even in winter. This disparity in the MLD causes differences in ecosystem dynamics between the northern and southern parts of the Japan Sea [Onitsuka and Yanagi, 2005]. The MLD drastically becomes shallow, less than 30-m depth, from March to April because of positive sea surface heat flux conditions in the whole area of the Japan Sea. The MLD remains shallow from May to October and gradually increases during November because of surface cooling and wind stress.
 Simulated monthly mean chl.a distributions are compared with those observed by the SeaWiFS (Figures 5 and 6) . Two phytoplankton blooms in spring (March to May) and autumn (October to December) are shown by the simulated and observed data. The spring phytoplankton bloom (>0.8 mg m−3) starts in March offshore of the TWC region, where the MLD is relatively shallow in winter. The spring bloom disappears from the south to north from May to June, together with depletion of DIN. Chl.a concentration remains low (<0.3 mg m−3) from July to September except for the eastern region off the Korean Peninsula in both the simulation and observation. Relatively high chl.a concentrations, corresponding to the autumn bloom, are distributed over a broad area, especially in the southwestern part of the Japan Sea as described by Yamada et al.  from November to December. The main reason for the generation of the autumn bloom is nutrient supply from the subsurface layer because of the deepening of the MLD [Onitsuka and Yanagi, 2005].
 The simulated vertical distributions of chl.a are compared with observed ones processed from the WOD98 along 135°E in February, May, July, and October (Figure 7). In February, relatively high chl.a is distributed in the upper 100-m depth in the southern area due to a shallower MLD than in the northern area. Although the spring bloom ends in the southern part, high chl.a concentrations continue to be seen in the northern part in May. Subsurface chl.a maximum is seen at a depth of about 30–50 m in July and October in both the simulation and observation.
 The simulated and observed vertical distributions of DIN (nitrate) along 135°E in February, May, July, and October are also shown in Figure 8. Although there are discrepancies between the simulated and observed DIN concentrations, especially in the northern part (>40°N), the model reproduces the major features seen in the observed nitrate levels. The 8.0 mmolN m−3 contour line lies at approximately a 100- to 150-m depth south of the subpolar front throughout the year, in both the simulated and observed distribution. Nitracline is seen at a 50-m depth especially in the northern part, which corresponds to the depth of the subsurface chl.a maximum.
 The TKS is practically the only entrance with flow into the Japan Sea. As described above, the TWC horizontally supplies heat, water, and materials through the TKS to the Japan Sea. The characteristics of the TKS must be described to identify nutrient sources in the surface layer of the Japan Sea. Physical and biological characteristics of the TKS are provided in Figures 9 and 10. These values were calculated at the western and eastern channels of the TKS, on either sides of the Tsushima Islands (Figure 11), and are substantially regarded as the boundary conditions for simulating ecosystem dynamics in the Japan Sea.
 The vertical profiles of total nitrogen concentration (DIN + PHY + ZOO + DET) show significant seasonal variations in both the western and eastern channels (Figure 9). The nitrogen profile is constant from surface to bottom in winter because of the deepening of the MLD, but the profile declines from spring to autumn, corresponding to the development of stratification. Surface nitrogen concentration is relatively high in winter and low in summer, in contrast, nitrogen concentration is relatively high from summer to autumn along the bottom. These profiles are nearly the same as those of DIN, which account for a large ratio of total nitrogen.
 The ratios of volume transports throughout the western and eastern channels are about 0.6 and 0.4, respectively, which are nearly the same as those observed by Takikawa et al.  (Figure 10). Seasonal variation differs between the volume and nitrogen transports. Total nitrogen transport through the TKS peaks in autumn. Nitrogen transport has a minimum value in July despite relatively large volume transport because materials such as nutrients are quite low in the surface layer, where current speed is relatively high in summer. The ratios of nitrogen transports through the western and eastern channels are consistent with those of volume transports.
4. Labeled Tracer Experiment
 Reproducible results are validated in the previous section. In the present section, we carry out a labeled tracer experiment to investigate the source of the nutrients consumed by phytoplankton. The experiment examines the influence of nutrients supplied by the TWC through the TKS and the upwelling along the east coast of Korea on the ecosystem dynamics in the Japan Sea.
 We introduced a set of artificial tracers (labeled according to specified region) similar to those applied to the western Arabian Sea by Kawamiya . The tracers are different from the ordinary passive tracers transported only by physical processes. They are transported through a combination of physical and biological processes. Three nutrient sources are considered in this study, the upwelling region of the Korean coastal region (EK) and the western and eastern channels of the TKS across the Tsushima Islands (WC, western channel; EC, eastern channel) (Figure 11). In the present experiment, we assume that nitrogen originating in each of the three sources is independent from each other.
 The formulation requires a calculation of the ratio of the nitrogen originally supplied in a certain area to the ambient nitrogen of the compartments of the ecosystem model. The formulation is almost the same as that in Kawamiya . The equation below denotes the case of the EK,
where Rki and Ci are the ratio and the concentration of each variable in the ecosystem model, respectively. Suffixes i and j vary from 1 to 4, when i = 1, the concentration Ci corresponds to DIN, 2 to PHY, 3 to ZOO, and 4 to DET. Sd is the sinking velocity of DET, δij is the Kronecker’s delta, Fj→i is the flux from compartments j to i through biochemical processes, and Fi→j is from i to j. The source term is written by,
where Δz is the thickness of the level, Rw1 and Re1 are the ratios of DIN from the WC and EC. The source term is set at 0, except for i= 1 in the case of the EK. The source term is calculated only when upward velocity across the depth of 70 m is positive in each grid of the EK. The depth of 70 m is determined by the maximum euphotic layer depth throughout the year in the Japan Sea [Onitsuka and Yanagi, 2005]. wC1Rk1 should be subtracted in the numerator because this flux is already taken into account in the second term of equation (4). In this case, wC1Rw1 and wC1Re1 are subtracted, and DIN labeled as the EK does not include those originating in the WC and EC. Thus the upward advection flux of DIN corresponds to the input flux of DIN because of the upwelling in the intermediate layer of the area EK.
 In the cases of the WC and EC, the ratio of Rk is replaced by Rw and Re in equation (4), respectively. The source terms are written as,
where λ is the longitude, ϕ is the latitude, R is the radius of the earth, Δλ and Δϕ are the horizontal grid sizes. Rk, Rw and Re are 0 in the upstream of WC and EC through the labeled tracer experiment. Unlike in the case of the EK, the source term is calculated for i= 1 to 4, which means all compartments across the boundaries of the WC and EC, because the penetration of the dissolved and particulate organic matters through the TKS becomes a consequential nutrient load because of decomposition of inorganic matter in the Japan Sea. The nitrogen fluxes from the WC and EC correspond to those in Figure 10.
 Integration of a labeled tracer experiment has been carried out for 12 years, from the beginning of the tracer input. While the gradient becomes stable after the 3-year run, the labeled DIN concentrations gradually increase for the period of this experiment (Figure 12). Labeled materials remain in the Japan Sea unless influx from three sources is fully discharged through the Tsugaru and Soya Straits. Results in the fourth year, when the gradient becomes stable, are shown in the next section.
4.2. Temporal and Spatial Variations of Labeled DIN
 The ratio of DIN concentration, originating in the EK, to the ambient DIN concentration is relatively high near the east coast of the Korean Peninsula throughout the year (Figure 13). The relatively high ratio appears near the coast in spring (May) and moves eastward along the TWC away from the Korean coast from summer (August) to autumn (November). The ratio decreases over the area in winter (February) because DIN supplied under the nitracline by the deepening of the MLD dilutes DIN labeled as the EK. The results suggest that the upward flux of DIN from the EK significantly affects biological productivity in the southwestern part of the Japan Sea from late spring to autumn, when there is no DIN supplied by the deepening of the MLD. In the present study, the main upwelling location (37°–39°N) seems to be somewhat different from previous reports (∼36°N), as shown in Figure 13. The upwelling of DIN in the EK does not include DIN originating in the WC and EC because the three nutrient sources are independent of each other. Although upwelling occurs in the southeastern part of Korea (∼36°N) in the simulation results, it is likely that a considerable amount of DIN upwelling in the southeastern part of Korea originates in the WC.
 DIN originating in the WC is distributed across a broad area in the southwestern Japan Sea (Figure 14). As in the case of the EK, the ratio is relatively high from spring to autumn but decreases in winter because of dilution by the deepening MLD. The TWC from the WC supplies a large amount of labeled DIN to the Japan Sea along the east coast of Korea and the shelf break off the southwestern Japanese coast. Hase et al.  found that the current flowing through the western channel feeds the second branch of the TWC, developing from spring to autumn along the shelf break off the Japanese coast. Morimoto et al.  reported that the second branch, fed from the western channel, plays an important role in the material transports from the TKS to the off San-in coast. The present study reveals that nutrients are supplied through the western channel to the broad area in the southern part of the Japan Sea as well as around the TKS.
 The ratio of the DIN originating in the EC is relatively higher than the other cases along the Japanese coast (Figure 15). A ratio above 0.4 is distributed in the nearshore regions along the Japanese coast in all seasons. The nutrient is suppressed by the shallow MLD even during the winter in this region. Consequently, although the TWC water is nutrient-poor, the ratio of DIN originating in the EC is elevated because of the relatively low DIN concentrations from other sources. These results suggest that the nitrogen flux from the EC plays an important role in the nutrient conditions of the nearshore region along the Japanese coast throughout the year.
4.3. Influence of Materials Transported Through the Tsushima/Korea Straits and Upwelling Along the East Coast of Korea on Biological Productivity
 Although the results of the labeled tracer experiment discussed above show the distribution and expansion of nitrogen originating from each source, their effects on biological productivity in the Japan Sea are not indicated. Therefore calculated annual primary production and primary production due to consumption of DIN originating in each of the three sources are shown in Figure 16. Annual primary production is high in the southwestern Japan Sea, supporting the spatial distribution of estimates calculated from the satellite ocean color images by Yamada et al. , while modeled production is somewhat underestimated when compared with the estimates by the satellite. This high primary productivity area corresponds to the high productivity area with sources from the EK and WC. The results suggest that the upward flux of DIN along the east coast of Korea and the nitrogen flux through the WC sustain the high primary production in the southwestern part of the Japan Sea.
 The contributions of the labeled nitrogen, originating from the three sources, to the annual primary production is shown in Figure 17. The low ratio in the northern part suggests other nutrient sources, thus in the northern part, nutrients are mainly supplied by the development of MLD from the intermediate layer. The area with a ratio above 60% is distributed in the whole of the southern Japan Sea. In particular, the area where the main nutrient source is either the WC or EC expands to the broad area in the southern Japan Sea. These results indicate that the materials transported through the TKS play a significant role in the biological productivity of the southern Japan Sea.
 It has been thought that the lower trophic ecosystem dynamics, especially two phytoplankton blooms, are caused by seasonal variations in MLD because of heat and fresh water supplied from the TKS. The influence of nutrients transported horizontally through the TKS on the biological productivity in the Japan Sea was not considered in the previous studies. However, the results described above suggest that the TWC affects biological productivity by transporting nutrients directly through the TKS as well as by changing hydrographic conditions through heat and fresh water transports.
 In recent years, concerns that the Three Gorges Dam constructed on the Changjiang River may affect the biological productivity in the East China Sea [Chen, 2000] and the hydrographic conditions in the Japan Sea [Nof, 2001] have emerged. Hence the oceanographic conditions of the TKS, the primary entrance to the Japan Sea, should be monitored in the short-term and long-term. The amount of existing biochemical data (for example, nutrients, chl.a) is much smaller than the hydrographic data (for example, current velocity, water temperature, salinity) at the TKS. The present study underlines the increasing importance of biochemical data at the TKS.
 The labeled DIN in the upper 100 m gradually increases during the integration period, as shown in Figure 12. Figure 18 shows the evolution of the extent of the influence by the three sources. The region with the ratio above 60% rapidly extends south of 40°N within a few years. After 4 years, the region gradually extends to the northeastern part of the Japan Sea. Consequently, it is likely that the effects of changes in the amount of materials transported through the TKS begin to appear in the southern part of the Japan Sea within a few years and gradually expand to the northern area over a decadal timescale, because the two dominant source regions, WC and EC, distribute across almost the entire southern Japan Sea area, except for the region around the subpolar front, as shown in Figure 17.
Yoo and Kim  indicated that the differences in spring bloom between 1997 and 1999 were related to the variability in volume transport and direction of the TWC in the southwestern Japan Sea. Kang et al.  reported that chl.a concentration and zooplankton abundance in the surface MLD were affected by the mesoscale eddy in the southwestern Japan Sea with data observed in 2000 and 2001. Another calculation of interannual variability using a high-resolution model that precisely describes the variability of the TWC and mesoscale eddies is needed. In the present study, we do not consider the input and output fluxes of nitrogen through the sea surface. Previous reports have indicated that atmospheric nitrogen, originating from the Asian continent, affects the surface nutrient conditions in the East China Sea [Nakamura et al., 2005]. Atmospheric nutrient input also may be considered as a nutrient source in the Japan Sea because of its proximity to the Asian continent.
 A nitrogen-based four-compartment coupled physical-ecosystem model is applied to the Japan Sea. Seasonal variability in the ecosystem characteristics simulated by the coupled model is in good agreement with the observations; temporal and spatial variations of chl.a concentrations in the surface layer, vertical profiles of chl.a and DIN, and regional differences in primary production are well reproduced. The results of the labeled tracer experiment indicate that one of the large nutrient sources in the southern Japan Sea is located along the east coast of Korea. The upward flux of DIN along the east coast of Korea and the nitrogen flux through the WC of the TKS sustain high primary productivity in the southwestern Japan Sea. The nitrogen flux from the EC of the TKS plays an important role in the surface nutrient conditions of the nearshore region along the Japanese coast throughout the year. The TWC affects biological productivity in the surface layer of the Japan Sea not only by changing hydrographic conditions through heat and fresh water transports but also by transporting nutrients directly through the TKS. Oceanographic conditions, including biochemical data at the TKS, should be monitored in both the short-term and long-term.
Appendix A: Appendix
 The biochemical processes in the four-compartment model are based on those developed by Kawamiya et al. . They are described as follows:
 Each term of the compartment is expressed in the equations below. Photosynthesis is doubled as the water temperature increases by 10°C [Eppley, 1972]. An almost identical assumption is adopted for other processes that depend on temperature. Parameters used in the ecosystem model are shown in Table 1.
where T is the water temperature, I is the light intensity, ke is the dissipation coefficient. The equation of photosynthesis has light inhibition in equation (A5) if light intensity I exceed Iopt. But we do not consider the light inhibition in the present study, thus if I exceed Iopt, we set I equal Iopt, because the simulated chl.a concentration in the surface layer does not match the observed one because of the effect of light inhibition from late spring to summer.
 We express sincere thanks to N. Hirose, J. Ishizaka, and H. Kawamura for helpful comments. We also thank the editor, the associate editor, and two anonymous reviewers for constructive comments. This work was partially supported by the Research fund from the Research Institute for Applied Mechanics, Kyushu University for the co-operative study among national institutes.