WITHDRAWN: A three-dimensional water quality model to evaluate the environmental capacity of nitrogen and phosphorus in Jiaozhou Bay, China

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Estuarine, Coastal and Shelf Science xxx (2014) 1e10

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A three-dimensional water quality model to evaluate the environmental capacity of nitrogen and phosphorus in Jiaozhou Bay, China Q2

Yan Li a, b, c, Keqiang Li a, *, Li Zhang a, c, Xiulin Wang a, Xiaoyong Shi a, Longjun Zhang c a

Key Laboratory of Marine Chemistry Theory and Technology, MOE, College of Chemistry and Chemical Engineering, Ocean University of China, Qing Dao 266100, China Research Vessel Centre of Ocean University of China, Qing Dao 266100, China c College of Environmental Science and Engineering, Ocean University of China, Qing Dao 266100, China b

a r t i c l e i n f o

a b s t r a c t

Article history: Accepted 20 June 2014 Available online xxx

Jiaozhou Bay has recently suffered from serious problems with pollution and eutrophication. Thus, landbased pollutant load must be reduced through a national control program. In this study, we developed a 3D water quality model to determine the environmental capacity of nitrogen and phosphorus in Jiaozhou Bay. A 3D hydrodynamic model (the estuarine, coastal, and ocean modeling system with sediments) was coupled with a water quality model, which was adapted from the dynamic model of nitrogen and phosphorus for a mesocosm near Jiaozhou Bay. The water quality model is divided into seven components: dissolved inorganic nitrogen, phosphate, phytoplankton, zooplankton, detritus, dissolved organic nitrogen, and dissolved organic phosphorus. Furthermore, it was calibrated based on data collected from Jiaozhou Bay in 2003. The proposed model effectively reproduced the patterns and values of the spatiotemporal variability in nutrient concentration and quantitative biomass, thus suggesting that a reasonable numerical representation of the prototype system must be developed for further evaluation of environmental capacity. © 2014 Published by Elsevier Ltd.

Keywords: water quality model nitrogen and phosphorus environmental capacity Jiaozhou Bay China

1. Introduction Most coastal areas worldwide have been damaged by pollution. As a result, commercial coastal and marine fisheries are significantly affected (Islam and Tanaka, 2004). To manage coasts sustainably and to protect fisheries and aquatic resources, aquatic pollution must be controlled. In the control of marine pollution (e.g., the US Total Maximum Daily Loads and the European Marine Strategy Framework Directive), the capacity of the marine environment for pollutants must be estimated because it is crucial to coastal water management and policy, as well as to the sustainable utilization of coastal areas (Borja et al., 2010; Han et al., 2011; Linker et al., 2013). Hence, the release, transport, and transformation of pollutants must be analyzed, and their effects on the corresponding ecosystems must be assessed (Islam and Tanaka, 2004). To conduct this analysis and evaluation, water quality modeling can contribute

* Corresponding author. E-mail address: [email protected] (K. Li).

strongly to the necessary scientific grounding of coastal management (Lung, 2001; Nobre et al., 2010; Shenk and Linker, 2013). Jiaozhou Bay is located in the southern coastal area of the Shandong Peninsula in China. It is semi-enclosed and is bordered by Qingdao City (Fig. 1). The bay is characterized by low turbidity, low amounts of suspended particulate matter, short and weak tides, and low waves and currents (Yang et al., 2004a,b). The bay has a surface area of 340 km2 and an average depth of 7 m. Furthermore, it is connected to the Yellow Sea by a 2.5 km long channel that extends 33 and 28 km from north to south and west to east, respectively (Song, 2010). Jiaozhou Bay is increasingly affected by anthropogenic activities. The sewage treatment plants in Tuandao, Haibo, and Licun generate various wastes and pollutants, which enter the bay through small seasonal rivers and streams, such as the Daguhe River, Moshuihe River, Loushanhe River, Licunhe River, and Haibohe River. Therefore, most of these rivers have become canals for industrial and domestic waste discharge because of economic progress and the increasing regional population (Liu et al., 2005). Consequently, eutrophication is a serious problem in Jiaozhou Bay given the concentrations of nitrogen and phosphorus, which have been increasing since the 1960s (Shen,

http://dx.doi.org/10.1016/j.ecss.2014.06.011 0272-7714/© 2014 Published by Elsevier Ltd.

Please cite this article in press as: Li, Y., et al., A three-dimensional water quality model to evaluate the environmental capacity of nitrogen and phosphorus in Jiaozhou Bay, China, Estuarine, Coastal and Shelf Science (2014), http://dx.doi.org/10.1016/j.ecss.2014.06.011

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then redistributed among different environmental phases. Thus, the physical marine environment must be adequately reproduced to simulate its biogeochemical features. To simulate the evolution of the transport and cycling of marine nutrients, a 3D water quality model coupled with a hydrodynamic model is ideal. The basic principles of this model involve mass conservation, the hydrodynamic equations of momentum and state, and the advectiondiffusion-reaction equations that describe the spatial and temporal distributions of each component (GESAMP, 1991; Moll and Radach, 2001). The computed profiles of temperature and diffusion are used as forcing functions in the sub-module of water quality. The 3D water quality model is then calibrated by comparing the predicted concentrations of nutrients and chlorophyll with the corresponding sets of field data. This methodology has two basic assumptions: (1) Phytoplankton (PPT) is considered one biota and is not distinguished in terms of species, size, and growth phase; (2) the nitrogen/phosphorus ratio of the uptake/excretion of dissolved inorganic nitrogen (DIN) and phosphate (PO4eP) by PPT conforms to the Redfield Ratio (16:1) and does not distinguish among ammonium-nitrogen, nitrite-nitrogen, and nitrate-nitrogen. 2.1. Hydrodynamic model

Fig. 1. Map of Jiaozhou Bay showing grid stations (▵) for cruises, Daguhe River, Moshuihe River, Loushanhe River, Licunhe River, Haibohe River, and the sewage treatment plants in Tuandao, Haibo, and Licun.

2001; Liu et al., 2005; Shen et al., 2006; Song, 2010). Thus, this bay requires a water quality model that evaluates the environmental capacity for nitrogen and phosphorus. In developing a water quality model, major physical, chemical, and biological processes should be considered to generate proper spatiotemporal resolutions. Moreover, the quantitative relationships between the response of water quality and external functions of force should be established to assess the environmental capacity of a system (Lung, 2001; Zou et al., 2006). In the field of water quality modeling, several related works have developed such models, including the bubble plume model (Imteaz and Asaeda, 2000), the sediment flux model, the corps of engineers integrated compartment water quality model (established in Chesapeake Bay) (Testa et al., 2013; Cerco and Noel, 2013), and the environmental fluid dynamics code model (Park et al., 2005). Although coupled physicalbiological models have been proposed for Jiaozhou Bay (Chen et al., 1999; Cui and Zhu, 2001; Wan et al., 2001), these models emphasized ecological processes and simplified the transformations of nitrogen and phosphorus. Hence, environmental capacity is difficult to estimate accurately. Given the weak hydrodynamic processes of this bay, the box models of nitrogen and phosphorus cycling could not effectively infer environmental capacity (Wu et al., 2001; Ren et al., 2003). Moreover, a 3D water quality model that focuses on the transport and transformation of nitrogen and phosphorus has not been established in Jiaozhou Bay. Therefore, this study mainly aims to generate such a model, which can be applied to coastal management and the evaluation of environmental capacity. We analyze and model nutrient and chlorophyll-a data collected from the bay in 2003. We then assess the proposed model using a similarity index and variation coefficients. 2. Methodology When nitrogen and phosphorus are discharged into the sea, they are transported and transformed in various ways. They are

The estuarine, coastal, and ocean modeling system with sediments (ECOMSED) (Blumberg and Mellor, 1987) simulates tidal and residual currents in the study areas. This model analyzes the hydrodynamic processes in the bay in 3D and calculates the flow field for the water quality model (Bao et al., 1999; Wan et al., 2003). We adopt an orthogonal system that is spatially curvilinear, with grids that measure 128
92 and a resolution ranging from a minimum of 284 m in Jiaozhou Bay to a maximum of 686 m near the boundary of the open ocean (Fig. 2). To obtain the vertical resolution, 11 slevels are generated in the water column, and the low boundaries are established at 0, 2, 4, 6, 8, 10, 15, 20, 25, 30, and 40 m. The model region ranges from 35.75  N to 36.24  N and from 120  E to 120.2

Fig. 2. Model grid of the proposed 3D hydrodynamic model for Jiaozhou Bay. The curvilinear orthogonal grid enables spatial variation in mesh resolution. It has a minimum grid spacing of 600 m and a minimum and maximum spacing of 284 and 686 m, respectively. In the model, 10 vertical s-levels are currently spaced evenly throughout the water column.

Please cite this article in press as: Li, Y., et al., A three-dimensional water quality model to evaluate the environmental capacity of nitrogen and phosphorus in Jiaozhou Bay, China, Estuarine, Coastal and Shelf Science (2014), http://dx.doi.org/10.1016/j.ecss.2014.06.011

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Y. Li et al. / Estuarine, Coastal and Shelf Science xxx (2014) 1e10  E. Given that the tidal current is the most stable and prevalent flow

among the external forces in the flow field of the studied area and that the M2 tidal component (main lunar, two tides per day) is predominant, the tidal amplitude and phase of M2 are applied in the open boundary (Bao et al., 1999). With respect to shallow water characteristics, Jiaozhou Bay is dominated by tides. River discharges are small and vary seasonally. Thus, the estuarine gravitational circulation or density flow is weak. The total terrigenous nutrient loads in Jiaozhou Bay can be evaluated by a barotropic model under constant temperature and salinity. The time increment is 186.3 s. To numerically assess the basic equations used in the current study, finite difference methods are used. The tide and residual current field are calibrated according to the ECOMSED-based hydrodynamic model proposed by Bao et al. (1999). The characteristics of the tide propagate into the bay from the Yellow Sea. The tide then turns clockwise as it travels toward the northern coast, whereas the residual current circulates weakly clockwise near the surface at a water depth of <10 m. This circulation is relatively stronger on the eastern side than on the western side (Bao et al., 1999; Wan et al., 2003). 2.2. Water quality model The water quality model evaluates the environmental capacity of the coastal area for nitrogen and phosphorus in terms of nutrient cycles and kinetics. This model has been successfully applied to the pelagic ecosystem of mesocosms near Jiaozhou Bay (Li et al., 2008). Fig. 3 shows the cycles of matter among water quality factors, primary producers and consumers, and various forces that affect the pelagic ecosystem of this water quality model. The model is divided into the following components: DIN, PO4eP, PPT, zooplankton (ZPT), detritus (DPT), dissolved organic nitrogen (DON), and dissolved organic phosphorus (DOP). The underlying environment is associated with sediments (e.g., benthic fluxes) and is considered an environmental variable (Wang et al., 2007). The water quality model examines five modules: PPT, ZPT, DIN, DON, and DPT. PPT growth is described by a synthesis function that depends on temperature, photosynthetically active irradiance, and nutrient availability. The temperature effect is exponential (Epply, 1972), and the inhibitory effect of high temperatures is neglected because PPT is a single component. To describe the light control of photosynthesis, Steele's function is used (Steele, 1962). Nutrient limitation is linearly proportional to concentration at low nutrient levels and approaches a constant value at high nutrient levels, as per the MichaeliseMenten equation. The equations and parameters are described at length in the Appendix.

Fig. 3. Schematic representation of the water quality model. The symbols are described in the Appendix.

3

PPT is lost through respiration and exudation, mortality, grazing, and sedimentation. All of these procedures affect the ecosystem differently (Fig. 3). Respiration is positively correlated with growth rate (Laws and Caperon, 1976), whereas exudation has a determinate proportional relationship with PPT biomass. For convenience, PPT metabolism (including respiration and exudation) is regarded as a single process that depends on light irradiance, temperature, and nutrient availability. Among these factors, light irradiance is decisive (Zlotnik and Dubinsky, 1989). Similarly, PPT mortality is a function of temperature (Epply, 1972; Jørgensen et al., 1991). The final two processes are generally associated with export production, either directly through deep sediment layers or indirectly toward high trophic levels and the egestion of fecal pellets. In ZPT grazing, the MichaeliseMenten formulation is modified (Fasham et al., 1990). Furthermore, a threshold is maintained for overgrazing (Radach and Moll, 1993; Imteaz et al., 2009). A constant fraction of the ingested food is assimilated, and the non-assimilated fraction is excreted as feces (Anderson, 1992; Imteaz et al., 2009). The excretions contain DIN and DON, and they are affected by ZPT biomass and size (Peters, 1983; Huntley and Boyd, 1984). For convenience, however, ZPT biomass alone is considered (Wen and Peters, 1994). This variable is also considered a function of temperature (Epply, 1972; Jørgensen et al., 1991). In the model, DIN and PO4eP are the major inorganic nutrients for algae. Hence, the uptake of nutrients by PPT is directly related to algae growth. PPT presumably assimilates nutrients according to a MichaeliseMenten dependence, and luxury consumption is not examined. Based on the resistance law, the uptake constants of half-saturated nitrogen and phosphorus concentrations are limiting. Therefore, they determine algal growth rate (Schnoor, 1996). The stock of nitrogen and phosphorus can be regenerated throughout the water column. A simple temperature-dependent formula describes the remineralization loops of organic nutrients and DPT without detailing the different chemical steps and microorganism species (Jones and Henderson, 1986; Chapelle et al., 1994). The equations and parameters are described at length in the Appendix. 2.3. Input data for modeling The main sources of nutrient pollutants are land-based input sources (Fig. 1), as well as the rivers, ditches, and treated wastewater that enter the bay. The DIN, DON, PO4eP, and DOP in the pollution loads were collected in March, May, July, August, October, and November by the Qingdao Environment Monitoring Center in Jiaozhou Bay. This center also surveyed the concentrations of DIN, PO4eP, and chlorophyll-a in the seawater in the spring (May), summer (August), and autumn (October) of 2003. These measurements are applied to calibrate and validate the model. The major parameters and input value definitions of the model are based on the mesocosm experiments conducted from 1999 to 2000 near Jiaozhou Bay (Table 1) (Li et al., 2008). Both the fluxes of open ocean and air-ocean boundaries are set to zero given their small contributions to the system overall. In the numerical domain, the initial distributions of the components of DIN, PO4eP, and PPT are presumably homogenous vertically and horizontally. The initial values of DIN, PO4eP, and PPT are based on the averages measured during early spring, namely, 500, 15, and 4 mg/l, respectively. We interpolate the data on water temperature and cloud cover with the horizontal and vertical grids of the hydrodynamic model. These data are obtained from the National Centers for Environmental Prediction (NCEP) and the National Center for Atmospheric Research Reanalysis Project (Kalnay et al., 1996). The temporal evolution of photosynthetically active irradiance, which was simulated using

Please cite this article in press as: Li, Y., et al., A three-dimensional water quality model to evaluate the environmental capacity of nitrogen and phosphorus in Jiaozhou Bay, China, Estuarine, Coastal and Shelf Science (2014), http://dx.doi.org/10.1016/j.ecss.2014.06.011

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Table 1 Values and units of parameters and sensitivity for DIN and PO4eP predictions to the parameter change. Parameter

r Iopt kPPT_G kPPT_D kPPT_Z kZPT_D kZPT_N kZPT_F kDPT_Z kDPT_B kDON_B kDOP_B KsN KsP KsDPT KsPPT  CPPT

GPPT_G GPPT_D GZPT_N GZPT_D GDON_B GDPT_B dPPT_ Z dDPT_Z rZPT_N

nS

Significance

Value

Photosynthetically active irradiance fraction of the total solar irradiance Optimal light irradiance Constant for phytoplankton growth rate Constant for phytoplankton mortality rate Constant for zooplankton grazing rate on phytoplankton Constant for zooplankton mortality rate Constant for zooplankton excretion rate Constant for zooplankton grazed rate by fish Constant for zooplankton grazing rate on detritus constant for detritus remineralization rate Constant for dissolved organic nitrogen remineralization rate Constant for dissolved organic phosphorus remineralization rate Half saturation constant for n-limitation Half saturation constant for p-limitation Half saturation constant for detritus-limitation Half saturation constant for ingestion Threshold for overgrazing on phytoplankton Temperature coefficient for phytoplankton growth Temperature coefficient for phytoplankton mortality Temperature coefficient for zooplankton excretion Temperature coefficient for zooplankton mortality Temperature coefficient for dissolved organic nutrient remineralization Temperature coefficient for detritus remineralization Assimilation efficiency for phytoplankton Assimilation efficiency for detritus Inorganic nutrient fraction of the excretion of zooplankton Phytoplankton or detritus sinking speed

Dobson and Smith's empirical function (Dobson and Smith, 1988), match the NCEP Reanalysis Project data in 2003 (RSD ¼ 27%) (Fig. 4). The pollutant loads are calculated according to the water flow rates observed and the pollutant concentration in each land-based source (Table 2). In 2003, the land-based loads of DIN, DON, PO4eP, and DOP were approximately 6502, 811, 346, and 329 ton/yr, respectively. During this period, the Haibo and Daguhe plants released their maximum nitrogen loads into the bay, whereas the Moshuihe plant discharged the maximum phosphorus load. In the model, the exchange rates of DIN and PO4eP are set to 0.1 ± 0.1 and 0.0005 ± 0.001 mg/m2$d, respectively, at the sedimentewater interface (Wang et al., 2007). These rates are affected by temperature with an exponential coefficient of approximately 0.05 1/ C (Radach and Moll, 1993). Once a quasi-steady state is reached on the 180th day after the calculation begins, calibration and verification are complete.

0.43 90 2.0 0.05 0.4 0.05 0.2 0.1 0.6 0.05 0.02 0.04 8 0.2 0.7 0.6 0.12 0.065 0.065 0.027 0.05 0.065 0.05 0.8 0.7 0.75 0.025

Unit

e W/m2 1/day 1/day 1/day 1/day 1/day 1/day 1/day 1/day 1/day 1/day mmolN/m3 mmolP/m3 mmolN/m3 mmolN/m3 mmolN/m3 1/ºC 1/ºC 1/ C 1/ºC 1/ºC 1/ºC e e e m/day

Confidence interval

±50% ±50% ±50% ±50% ±50% ±50% ±50% ±50% ±50% ±50% ±50% ±30% ±50% ±50% ±50% ±50% ±50% ±50% ±50% ±50% ±50% ±50% ±50% ±50% ±50% ±50% ±50%

Coefficients of variation DIN

PO4eP

0.99 0.87 0.92 0.13 0.38 0.44 0.38 0.32 0.43 0.28 0.34 e 0.1 0.18 0.28 0.064 0.00033 0.42 0.20 0.36 0.36 0.48 0.28 0.44 0.40 0.11 0.37

2.10 2.78 2.74 0.40 0.69 0.41 0.50 0.23 0.29 0.11 e 1.76 0.25 0.49 0.11 0.068 0.0011 1.96 0.63 0.54 0.18 1.13 0.28 0.28 0.19 0.25 1.22

In the sensitivity analysis, the Monte Carlo analysis (Harmon and Challenor, 1997) states that the alteration of a single parameter in a model influences a given component if all other variables remain constant. In the model, one parameter in the model is modified 100 times, and a typical mean value is assumed for the parameter. With respect to parameter uncertainty, a default confidence interval is also set at 50% of the mean. If the CV-value exceeds 0.5, then the component is sensitive to the analyzed parameter. If the CV-value is between 0.1 and 0.5, then the component is relatively sensitive. Finally, the component is insensitive if the CV-value is less than 0.1. Based on the presuppositions above, the DIN and PO4eP predictions are sensitive to the values selected for the fractions of total solar irradiance (r), optimal light irradiance (Iopt), and PPT growth rate constant (kPPT_G) that display photosynthetically active irradiance. This finding indicates that the concentrations of DIN and PO4eP are strongly correlated with light irradiance and PPT growth.

3. Results and discussion 3.1. Sensitivity analysis Numerical models rely on experimentally determined parameters. Uncertainty is the result of measurement errors and the technical incapability of measuring relevant processes and experimentally reproducing natural conditions. When parameters are not experimentally determined but are instead fitted through calibration, uncertainty is linked to the difficulty of estimating the best fit of the model to the data (Tusseau et al., 1997). This uncertainty can be managed by calculating the coefficient of variation (CV) of the model components based on the Monte Carlo analysis of sensitive parameters (Hakanson and Peters, 1995; Hakanson, 2000). This process uses Modelmaker 4.0 software (Cherwell Scientific Ltd.) to conduct a systematic sensitivity analysis of the most sensitively fitted parameters (Table 1).

Fig. 4. Data from the NCEP Reanalysis Project (hollow round) and the 2003 simulation of the temporal evolution of photosynthetically active irradiance (line) in Jiaozhou Bay.

Please cite this article in press as: Li, Y., et al., A three-dimensional water quality model to evaluate the environmental capacity of nitrogen and phosphorus in Jiaozhou Bay, China, Estuarine, Coastal and Shelf Science (2014), http://dx.doi.org/10.1016/j.ecss.2014.06.011

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Table 2 Concentrations and fluxes of nutrients on land-based sources entering Jiaozhou Bay in 2003. Source

Daguhe River

Moshuihe River

Concentrations of nutrients (mg/l) dissolved inorganic nitrogen (DIN) 15.9 ± 13.3 22.5 ± 5.7 Total dissolved nitrogen (TDN) 17.8 ± 13.0 23.0 ± 5.3 Phosphate (PO4eP) 0.40 ± 0.55 3.18 ± 0.82 Total dissolved phosphorus (TDP) 1.29 ± 1.83 3.74 ± 0.82 Water discharge (m3/s) 5.65 ± 6.15 2.11 ± 0.68 Fluxes of nutrients (ton/yr) Dissolved inorganic nitrogen (DIN) 1397 1147 Dissolved organic nitrogen (DON) 201 30 Phosphate (PO4eP) 57 168 Dissolved organic phosphorus (DOP) 114 26

Loushanhe River

Licunhe River

Licun plant

Haibohe River

Haibo plant

Tuandao plant

16.9 ± 8.2

25.8 ± 9.7

14.0 ± 19.8

28.1 ± 15.1

55.7 ± 18.0

7.1 ± 9.2

20.7 ± 7.3

29.1 ± 11.1

18.2 ± 28.5

34.7 ± 17.5

59.0 ± 18.9

10.4 ± 11.8

0.27 ± 0.28

0.96 ± 1.02

0.40 ± 1.12

1.29 ± 1.51

0.91 ± 1.34

1.17 ± 1.70

1.05 ± 0.71

2.67 ± 0.57

0.63 ± 1.25

3.24 ± 1.89

1.31 ± 1.40

2.20 ± 2.73

0.91 ± 0.28

1.41 ± 0.60

0.53 ± 0.07

0.76 ± 0.61

0.84 ± 0.09

0.41 ± 0.17

468

1074

231

630

1476

79

6502

132

130

68

130

76

44

811

10

37

7

25

25

17

346

22

83

4

63

11

6

329

3.2. Simulation of the temporal and spatial distribution of nutrients Figs. 5e7 depict the DIN, PO4eP, and chlorophyll-a in the model and on the field surface during the spring, summer, and autumn of 2003, respectively. DIN concentrations were high near the sources of the estuaries (ranging from 100 mg/l to 1000 mg/l) given allochthonous input sources such as rivers and treated wastewater. By contrast, these concentrations decreased in the outer part of the bay as a result of the dilution and diffusion induced by the rapid exchange current of seawater flowing through the narrow channel (Fig. 5). DIN concentrations were at their maximum in autumn; they exceeded Grade II (300 mg/l) of the quality standards of

Total

Chinese seawater. In spring, these concentrations were confined to the northern part of the bay (Fig. 5A and D); however, they extended well into the middle of the bay during summer and autumn (Fig. 5B,C,E and F) because of the large amount of freshwater discharged and the heavy DIN load. In autumn, PO4eP concentrations were at their highest, exceeding Grade II (30 mg/l) of the quality standards of Chinese seawater (Fig. 6). In summer, these concentrations (ranging from 2 mg/l to 20 mg/l) were confined to the western part of the bay (Fig. 6B and E). They then moved to the eastern part of the bay in spring and autumn (Fig. 6A,C,D and F). PPT biomass, which is represented by chlorophyll-a concentration, was high in the northern part of the bay in summer, as was nutrient

Fig. 5. Simulated (top) and observed (bottom) distributions of surface DIN in Jiaozhou Bay during the spring, summer, and autumn of 2003. (unit: mg/l).

Please cite this article in press as: Li, Y., et al., A three-dimensional water quality model to evaluate the environmental capacity of nitrogen and phosphorus in Jiaozhou Bay, China, Estuarine, Coastal and Shelf Science (2014), http://dx.doi.org/10.1016/j.ecss.2014.06.011

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Fig. 6. Simulated (top) and observed (bottom) distributions of surface PO4eP in Jiaozhou Bay during the spring, summer, and autumn of 2003. (unit: mg/l).

loading (Fig. 7B and E). In spring and autumn, the increase became gradual and was restricted to the northeastern part of the bay (Fig. 7A,C,D and F). As a result, nutrient concentrations increased in autumn as the PPT died (Figs. 5 and 6).

The overall pattern of model results matches not only observations regarding the spatial distribution trends, but also those related to the plankton dynamics in Jiaozhou Bay; that is, the idea that PPT increases sharply during seasons in which nutrient loading

Fig. 7. Simulated (top) and observed (bottom) distributions of surface chlorophyll-a in Jiaozhou Bay during the spring, summer, and autumn of 2003. (unit: mg/l).

Please cite this article in press as: Li, Y., et al., A three-dimensional water quality model to evaluate the environmental capacity of nitrogen and phosphorus in Jiaozhou Bay, China, Estuarine, Coastal and Shelf Science (2014), http://dx.doi.org/10.1016/j.ecss.2014.06.011

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is high. Unlike observation data, however, our model persists that in spring, chlorophyll-a and nutrient concentrations are high and low, respectively. Furthermore, DIN concentration is high in summer and low in autumn in the northern part of the bay (Figs. 5A, 6A and 7A). This discrepancy may be attributed to the inadequacy of the land-based data that was monitored. In particular, we lack data on the accurate and continuous flow of water. The modeled chlorophyll-a concentration also deviates from the observed values, particularly in summer (Fig. 7). This finding may be related to the extremely low values of the simulated PO4eP values in the northeastern part of the bay (Fig. 6). Area growth may also be limited by factors such as suspended matter and silicate. 3.3. Quantitative assessments Numerical models are used in environmental and ecological management. Therefore, (1) model simulations/predictions must be based in reality and (2) uncertainties in model simulations/ predictions must be quantified (Fitzpatrick, 2009). These considerations are associated with the difficulty of estimating the model that best fits with the data (Tusseau et al., 1997). Aside from assessment techniques, many simple, quantitative metrics can assess model skill (Stow et al., 2003), including relative standard deviation (RSD) and the Pearson correlation (R) in relation to the predictions of the model and the observation data. The use of several metrics simultaneously thoroughly evaluates skill because the different performance aspects of the model can be captured. The similarity index (from Shimadzu Scientific Instruments) is a quantitative metric that can assess model skill, as described by Millie et al. (1997) and Kirkpatrick et al. (2000). The modeling patterns are similar to absorption spectra and distribute spatially at various magnitudes (Millie et al., 1997). The similarity index of the model (SI) is generated by computing the angle between the vectors composed of the observations and the simulations/predictions as follows:

2

3

6 7 Pn o p 6 7 ðCi
Ci Þ i¼1 7 2
arccos6 6qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 7 Pn P 2 n p 2 o 4 5 C
C ð Þ ð Þ i i i¼1 i¼1 SI ¼ 1 

(1)

p

where n denotes the number of observations, and Cio and Cip correspond to the ith observation and simulation data, respectively. The arc-cosine transformation and division by p/2 shifts from a nonlinear (cosine of the angle) to a linear result between zero and one. SI varies from one to zero; the former represents identical modeling, whereas the latter indicates poor modeling. The simulation results of the 3D model are compared with the observed data regarding nutrient and chlorophyll-a surface distribution. These data were collected during spring, summer, and autumn (Table 3). The simulated DIN patterns and values match the Table 3 The Relative Standard Deviation (RSD), the Pearson correlation (R) and similarity index (SI) between observed and simulated data of temporal variation of surface dissolved inorganic nitrogen (DIN), phosphate (PO4eP) and chlorophyll-a (Chl-a) in 2003 and spacial distribution of DIN, PO4eP and Chl-a in spring (Spr.), summer (Sum.) and autumn (Atu.) 2003 in Jiaozhou Bay. Variable

DIN

Season RSD/100% R SI

Spr. 20 0.88* 0.84

*

PO4eP Sum. 26 0.68* 0.74

Aut. 42 0.39 0.63

Spr. 43 0.32 0.59

Chl-a Sum. 79 0.23 0.45

Aut. 33 0.28 0.55

Correlation is significant at the 0.05 level (2-tailed).

Spr. 68 0.03 0.49

Sum. 59 0.26 0.46

Aut. 62 0.7* 0.68

7

observed values reasonably well, and their surfaces share similar spatial distribution trends and magnitudes (RSD ¼ 29% ± 11%, R ¼ 0.65 ± 0.25, SI ¼ 0.74 ± 0.11). However, the simulated PO4eP and chlorophyll-a values are dissimilar to the observed values (RSD ¼ 57% ± 17%, R ¼ 0.30 ± 0.22, SI ¼ 0.54 ± 0.09). Thus, the model must be improved although it is acceptable for environmental capacity evaluation. 3.4. Application in the evaluation of environmental capacity With respect to the evaluation of the environmental capacity of a bay for pollutants, the key procedures are the self-purification of the physical, chemical, and biology processes and the establishment of quantitative relationships between the response of water quality and pollution sources. Based on the concept of environmental capacity (GESAMP, 1986), this capacity can be calculated as the maximum amount of pollutants in a target coastal region under a given criterion and time period. This process includes the selfpurification and output of pollutants in a marine system. Once calibrated and validated, the model is reconfigured to simulate the concentration field of pollutants for environmental capacity evaluation. This capacity can then be computed by integrating the grades of the pollutant concentration field temporally and spatially using the proposed 3D water quality model (Li and Wang, 2013). To reduce pollutant loads and satisfy the criteria for water quality, a control plan for total pollutant load must be established in the study area. Moreover, we can estimate environmental capacity and simulate the response fields of pollution sources to maximize total allocated loads using the proposed 3D water quality model (Han et al., 2011). 4. Conclusions In this study, a 3D water quality model is presented to describe nutrient transport and transformation in a coastal pelagic ecosystem that is semi-enclosed. This model is divided into seven components (DIN, PO4eP, DON, DOP, PPT, ZPT, and DPT). After the model was calibrated for Jiaozhou Bay based on seasonal observations (spring, summer, and autumn), the results suggested that the model could favorably simulate relevant nutrient distributions. The model is acceptable but the quantitative assessments (RSD, R, and SI) are unsatisfactory. Thus, it must be enhanced further. The sensitivity of the DIN and PO4eP predictions to changes in the parameters is examined as per the Monte Carlo analysis. These analyses are necessary in the investigation of the control mechanism of nutrient cycling in Jiaozhou Bay, as well as other coastal waters in China. Acknowledgments The authors would like to thank Dr. Xianwen Bao for proposing the hydrodynamic model (ECOMSED) for application in Jiaozhou Bay, as well as Dr. Xiuquan Wan for his assistance during the modeling process. The authors also gratefully acknowledge the Qingdao Environment Monitoring Center for providing the data on river water and waste discharge and concentration distributions. This work was supported by the National Natural Science Foundation of China (No. 41340046 and U1406403), Science Fund Projects of Shandong Province (No. ZR2010DM005), Science and Technology Development Plan of Qingdao (No. 11-2-3-66-nsh), and Fundamental Research Funds of the Ocean University of China (No. 201362014). Modeling was conducted in the Computing Services Center of the Ocean University of China.

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 . DPO4 P ¼  mPPT_G CPPT þ rZPT_N mZPT_N CZPT rN=P þ mDOP_B CDOP

APPENDIX Mathematical formulation of the model

þ SPO4 P

The water quality model applies the outputs of the physical model, namely, convection and dispersion motions, temperature, and photosynthetically active irradiance. The general evolution equation for the variation in the concentration of standing stock C at any given time is given by:

    vC vC vC vC v vC v vC ¼ u v w þ Ah þ Ah vt vx vy vz vx vx vy vy   v vC þ Av þ S þ Dbiogeochem vz vz

(A.5)   DDON ¼ mPPT_E CPPT þ 1  rZPT_N mZPT_N CZPT þ mDPT_B CDPT  mDON_B CDON þ SDON (A.6)    . DDOP ¼ mPPT_E CPPT þ 1  rZPT_N mZPT_N CZPT þ mDPT_B CDPT rN=P

(A.1)

 mDOP_B CDOP þ SDOP (A.7)

where C denotes the concentration of a component; t corresponds to time; u, v, and w are the mean velocity components; Ah and Av represent the diffusion coefficients of the horizontal and vertical eddies, respectively; S denotes the source term; and Dbiogeochem represents the biogeochemical variation term. The standing stock of each component is predicted according to temporal and spatial changes by inputting velocity components that were calculated by hydrodynamic modeling and incorporated into the water quality model. The formulations of the components are presented in Eqs. (A.2)e(A.8).

   DPPT ¼ mPPT_G  mPPT_E  mPPT_D CPPT  mPPT_Z CZPT  nS vCPPT vz (A.2) where expressions of PPT growth rate, metabolizing rate, mortality rate, and the grazing rate of ZPT on PPT are given by Epply (1972), Laws and Caperon (1976), Baretta et al. (1988) and Radach and Moll (1993):

mPPT_G ¼ kPPT_G f ðTÞPPT_G f ðIÞPPT_G f ðNÞPPT_G mPPT_E ¼ rPPT_E mPPT_G mPPT_D ¼ kPPT_D eðGPPT_D T Þ

mPPT_Z ¼

8 > < kPPT_Z > :

 CPPT  CPPT  CPPT  CPPT þ KsPPT

0

þ mPPT_D CPPT  mDPT_B CDPT  ðnS =HÞðvCDPT =vzÞ

(A.8)

where expressions of DON, DOP, and DPT remineralization rate are given by Jones and Henderson (1986) and Chapelle et al. (1994):

mDON_B ¼ kDON_B eGDON_B T mDOP_B ¼ kDOP_B eGDON_B T mDPT_B ¼ kDPT_B eGDPT_B T and SDIN, SPO4 P , SDON, and SDOP are nitrogen and phosphorus loads, and H denotes the total water depth (sea level plus free surface elevation). Photosynthetically active irradiance is the primary source of energy for autotrophic organisms and is generated by solar radiation that reaches the sea surface at wavelengths ranging from 400 nm to 700 nm. The strength of solar radiation penetration on the sea surface is influenced by the ellipticity of the Earth's orbit, the absorption of atmospheric clouds, and solar altitude. To describe available irradiance at the sea surface, Dobson and Smith's empirical function (Dobson and Smith, 1988) is used:

 CPPT  CPPT

I ¼ Q0 Sh ðA þ BSh Þð1  RÞ

 CPPT < CPPT

where Q0 (¼1368 W/m2) denotes a solar constant (Sellers, 1965); R (¼0.378) represents the albedo of the sea surface (Pan, 1987); A and B are the parameters of cloud amount (Dobson and Smith, 1988); and Sh corresponds to the sine angle between the sun and the local normal vector, which depends on 4, q, and t:

 DZPT ¼ dPPT_Z mPPT_Z þ dDPT_Z mDPT_Z  mZPT_D  mZPT_N   kZPT_F CZPT

(A.3)

where expressions regarding ZPT grazing in relation to DPT, mortality, and excretion rates are given by Fasham et al. (1990), Jørgensen et al. (1991) and Wen and Peters (1994):

mDPT_Z ¼ kDPT_Z

   DDPT ¼ mZPT_D þ 1  dPPT_Z mPPTZ dDPT_Z mDPT_Z CZPT

CDPT CDPT þ KsDPT GZPT_D T

mZPT_D ¼ kZPT_D e

mZPT_N ¼ kZPT_N eGZPT_N T DDIN ¼ mPPT_G CPPT þ rZPT_N mZPT_N CZPT þ mDON_B CDON þ SDIN (A.4)

Sh ¼ sinh ¼ sin4sinqþcos4cosq cos t

(A.9)

(A.10)

where 4 denotes the geographical latitude; q is the equator latitude that ranges from þ23.50 (the summer solstice) to 23.50 (the winter solstice); and t represents daytime:

q ¼ arcsin½sinð23:5p=180Þsinð2pðtd  81Þ=365Þ

(A.11)

t ¼ pðth  4Þ=12  l

(A.12)

where td denotes the time of the year expressed in days; th is the time of the day expressed in hours; and l (¼8p/12) represents the geographical longitude in Jiaozhou Bay. For convenience, t is taken as the angle between p and p, with t ¼ 0 at noon. The photosynthetically active irradiance at sea surface is then given by:

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IPA ¼ Ir ¼ Q0 rSh ðA þ BSh Þð1  RÞ IPA ¼ 0

if Sh > 0 if Sh  0

(A.13)

The irradiance just below the water surface is reduced as depth €h et al., increases, according to an exponential equation (Ebenho 1997) based on the light extinction coefficient:

IH ¼ IPA

1 H

ZH

ekz dz

(A.14)

0

where H denotes the water depth, and k represents the coefficient of light extinction, which is mainly proffered by chlorophyll selfshading (Riley, 1956):

  2=3 k ¼ k0 þ k1 rChl=PN CPPT þ k2 rChl=PN CPPT

(A.15)

where k0 (¼0.8 1/m) is the coefficient of water self-extinction; k1 [¼0.0088 1/m$(mg Chla)] and k2 [ ¼ 0.054 1/m$(mg Chla)2/3]. These coefficients are self-shading chlorophyll (Riley, 1956). In addition to photosynthetically active irradiance, temperature and nutrient availability affect PPT growth. Steele's function describes the light control in photosynthesis (Steele, 1962):

f ðIÞPPTG ¼

  IH I exp 1  H Iopt Iopt

(A.16)

The temperature effect is exponential (Epply, 1972):

f ðTÞPPTG ¼ eGPPT_G T

(A.17)

Nutrient limitation is computed by the MichaeliseMenten equation, and the total nutrient limitation can follow either the minimum, multiplication, or resistance law (Schnoor, 1996). The resistance law is illustrated below:

f ðNÞPPTG ¼

CPO4 P CDIN CDIN þKsN CPO4 P þKsP CDIN CDIN þKsN

CPO4 P þKsP 4 P

þ CPO

(A.18)

PPT metabolizes through photosynthesis and depends on light irradiance, temperature, and nutrient availability. Among these, light irradiance is the decisive factor (Zlotnik and Dubinsky, 1989). The ratio of PPT metabolism in photosynthesis is expressed by Eq. (A.19):

rPPT_E ¼

0:24Iopt  1:2 0:12 I þ 10  Iopt H Iopt  10

(A.19)

Therefore, we modify the MichaeliseMenten formulation for grazing: the remineralization of organic nutrients and DPT, PPT, and ZPT mortality are all described by temperature-dependent formulae. Sink terms are generally described using first-order kinetics through the variables PPT and DPT (A2 and A8). Sedimentation is a vertical flux that can be treated as an advection with a speed of ns (Table 1).

8 vðnS CPPT Þ vC > > ¼ nS PPT < vz vz sedi ¼ > vðn C Þ vC > DPT :  S DPT ¼ n S vz vz

(A.20)

The initial values of these parameters have been determined through field and parallel laboratory experiments and have been optimized by modeling and sensitivity analysis based on prior

9

mesocosm experiments near Jiaozhou Bay (Li et al., 2008). Table 1 lists the significance of the parameters, units, and values.

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Please cite this article in press as: Li, Y., et al., A three-dimensional water quality model to evaluate the environmental capacity of nitrogen and phosphorus in Jiaozhou Bay, China, Estuarine, Coastal and Shelf Science (2014), http://dx.doi.org/10.1016/j.ecss.2014.06.011

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