*2.4. Method to Estimate the MEC*

The marine environment capacity (MEC) is decided by the following factors:


The response coefficient method is adopted here for the research on environment capacity. By taking residual capacity maximum as principal, this study has Sanmen Bay for example, and then calculates the distribution of the marine environment capacity of Sanmen Bay.

Given that velocity and diffusion coefficient is determined, a convection-diffusion equation can be regarded as a linear equation.

The formula is shown as follows:

$$\mathbb{C}(x, y, z) = \sum\_{i=1}^{m} \mathbb{C}\_{i}(x, y, z) \tag{3}$$

where *C*(*x*, *y*, *z*) means the concentration of each position (mg/L). *Ci*(*x*, *y*, *z*) means the concentration of the *i*th position (mg/L).

The concentration field formed separately by each source can also be regarded as some times of the one formed when a certain source strongly discharges pollution.

$$\mathbf{C}\_{i}(\mathbf{x}, \mathbf{y}, \mathbf{z}) = \mathbf{Q}\_{i} \cdot \mathbf{a}\_{i}(\mathbf{x}, \mathbf{y}, \mathbf{z}) \tag{4}$$

where *Q<sup>i</sup>* is the *i*th pollution source's emission; *α<sup>i</sup>* is the response coefficient field of the *i*th pollution source, referring to one point's concentration under unit source intensity. *α<sup>i</sup>* reflects the *i*th point's response level to the *i*th pollution source.

According to the response coefficient and controlling goals of each controlling point, to work out the environment capacity by the linear programming method. The main steps are as follows:


Taking Sanmen Bay, for example, this paper studies total amount control and emission cutdown management. One of the central basis of management of the marine environment is environment capacity. Contaminants picked to be calculated should reflect the water quality, degree of contamination, and operability on the management of environment capacity and contamination controlling and other aspects. Considering pollution source, the water quality of Sanmen Bay, and linking to the control index of land-sourced pollutants, Sanmen Bay's prime pollutants are nutrient salt formation such as nitrogen, phosphorus, etc. COD is a comprehensive index to describe the degree of water pollution. According to relevant provisions, CODs, (chemical oxygen demand) TN (total nitrogen), and TP (total phosphorus) should be taken into consideration in calculation of environment capacity or cutdown. Based on investigations of Sanmen Bay and relevant provisions on seawater quality, this paper will calculate by controlling the content of CODMn, inorganic nitrogen

and labile phosphate in seawater and then gets a result. Finally, the research will make a conversion from the result to environment capacity or cutdown for COD, TN, and TP.

#### **3. Results**

#### *3.1. Hydrodynamics in the Bay*

Field Observation and Analysis

Surface water elevations were measured by WSH at the Jiantiao station and Gangdi station, both recorded at a 60-min sampling interval. The velocity data discussed in this paper are measured by ADP at 400 KHz and 600 KHz in these two stations.

The tidal characteristic values of Jiantiao Station and Gangdi Station are less than 0.5, so it can be inferred that the tide of Sanmen Bay belongs to the regular semidiurnal tide (Table 2).

**Table 2.** Tidal eigenvalue (*HO*<sup>1</sup> , *HK*<sup>1</sup> and *HM*<sup>2</sup> means the amplitudes of *H*<sup>1</sup> , *O*<sup>1</sup> and *M*<sup>2</sup> respectively).


The current property ratios ((*W*O1 + *WK*1)/W*M*2) of L1, L2, and L3 are all less than 0.5, indicating that the *M*<sup>2</sup> tidal component of Sanmen Bay is dominant and is the main tidal component. The tidal current type of Sanmen Bay belongs to the regular half day tidal current. Generally, the bay is greatly affected by the tidal component of the shallow sea. The calculation results also prove this point. Among them, the value (*WM*4/*WM*2) of theL1 station is the smallest. This is mainly because the L1 station is located at the mouth of Sanmen Bay, with an open water surface and deep depth, so it is less affected by the tidal component of the shallow sea (Table 3).

**Table 3.** Tidal current eigenvalue (*WO*<sup>1</sup> , *WK*<sup>1</sup> and *WM*<sup>1</sup> means the length of long semi axis of partial current ellipse of *O*<sup>1</sup> , *K*<sup>1</sup> and *M*<sup>1</sup> respectively).


#### *3.2. Model Result Hydrodynamics in the Bay*

Figure 5 shows the torrent velocity vector of ebb and flood tide during spring and neap tide in December 2009.

bay from east to west via Shipu Port. The two flood tides merge in the bay and then divide into four flows towards the summit of the bay. The first one flows into Jiantiao Harbor, the second one flows into Qimen Harbor and Haiyou Harbor through the Shepan water channel, the third one flows into Liyang Harbor and Qingshan Harbor, the fourth one flows into Baijiao water channel. The direction of the flood tide in each port branch is basically parallel to the longitudinal axis of the port branch, and the velocity is similar to that of the flood flow in the open sea. On the large area of shallow shoals which are apart

During the ebb flow, the flow direction is basically opposite to that of flood flow, and the main stream is along southeast. The water at the bay summit leaks out of the trough. After the ebb tides converge, most of them flow out of the Sanmen Bay mouth in the southeast direction, and a small part of it flows out from west to east via Shipu Port. The Yushan Islands which is in the southeast corner of the calculation area and the Dongji Islands in the southwestern part are both affected by the underwater topography, and the direction of the flood and ebb tides change to a certain extent, and the local currents are

from the port branch, the floodplain shows a slow flow and diffusing state.

relatively complicated.

**Figure 5.** Depth-average velocity vectors during flood and neap (the entire domain). ((**a**,**b**) flood spring and flood ebb, (**c**,**d**) neap spring and neap ebb). **Figure 5.** Depth-average velocity vectors during flood and neap (the entire domain). ((**a**,**b**) flood spring and flood ebb, (**c**,**d**) neap spring and neap ebb).

*3.3. Water Exchange Ability in the Bay* Luff et al. (1996) introduced the concept of the Half-life period, which is defined as the time required for the concentration of the conservative substance to be diluted to half of the initial concentration by convection diffusion. The definition is based on the fact that it is almost impossible for the final concentration of a substance to be zero, and the rate of dilution represents the rate of water quality change, that is, the exchange capacity of the sea area. Based on the concept of half exchange time, this study calculated the diffusion, transport, and dilution speed of conservative matter in each grid point of Sanmen Bay by After the tidal waves propogate from the outer sea into Sanmen Bay through southeast to the northwest, the tidal motion characteristics are formed mainly with standing waves in the bay, while ebb and flood last little. The tidal current in Sanmen Bay is basically reciprocating, and the flow direction is mostly influenced by the topography. The flood tide flowing into the bay mouth is mainly in the northwest direction, and the ebb tide is mainly in the southeast direction. The water channels and harbor branches are basically along the longitudinal axis, among them Shipu Harbor's flood tide flow to the west, and ebb tide flow to the east. The open sea area from the bay mouth to the outer bay shows swirling current characteristics in different degrees.

During the flood period, the East China Sea tide waves propagate from the southeast side of the large area along the northwest direction, which mainly enters Sanmen Bay through its mouth. Most of the flood tide flows into the bay in the northwest through the bay mouth after passing through the Maotou Sea. A small part of the tide flows into the bay from east to west via Shipu Port. The two flood tides merge in the bay and then divide into four flows towards the summit of the bay. The first one flows into Jiantiao Harbor, the second one flows into Qimen Harbor and Haiyou Harbor through the Shepan water channel, the third one flows into Liyang Harbor and Qingshan Harbor, the fourth one flows into Baijiao water channel. The direction of the flood tide in each port branch is basically parallel to the longitudinal axis of the port branch, and the velocity is similar to that of the flood flow in the open sea. On the large area of shallow shoals which are apart from the port branch, the floodplain shows a slow flow and diffusing state.

During the ebb flow, the flow direction is basically opposite to that of flood flow, and the main stream is along southeast. The water at the bay summit leaks out of the trough. After the ebb tides converge, most of them flow out of the Sanmen Bay mouth in the southeast direction, and a small part of it flows out from west to east via Shipu Port. The Yushan Islands which is in the southeast corner of the calculation area and the Dongji

Islands in the southwestern part are both affected by the underwater topography, and the direction of the flood and ebb tides change to a certain extent, and the local currents are relatively complicated.

#### *3.3. Water Exchange Ability in the Bay*

Luff et al. (1996) introduced the concept of the Half-life period, which is defined as the time required for the concentration of the conservative substance to be diluted to half of the initial concentration by convection diffusion. The definition is based on the fact that it is almost impossible for the final concentration of a substance to be zero, and the rate of dilution represents the rate of water quality change, that is, the exchange capacity of the sea area.

Based on the concept of half exchange time, this study calculated the diffusion, transport, and dilution speed of conservative matter in each grid point of Sanmen Bay by using the transport and diffusion model of conservative materials, so as to study the water exchange capacity of Sanmen Bay.

#### 3.3.1. Passive-Tracer Concentrations

Based on the previous hydrodynamic model, the water exchange model for the transport of regional passive-matter concentration is established (Figure 1c). *Water* **2022**, *14*, x FOR PEER REVIEW 11 of 19

> In the closed boundary condition, the current is 0 ( *<sup>∂</sup><sup>C</sup> <sup>∂</sup><sup>n</sup>* = 0), different treatment methods are adopted for the inflow and outflow of the model, and the inflow material concentration is 0, and the outflow material concentration is calculated by the model. The flow conditions are automatically obtained from the flow model. west of the Bay. It can be considered that the water exchange in Sanmen Bay has been basically completed at this time. port in the bay head has dropped below 0.1 unit.

> According to the conservative material model, the whole continuous tidal process is applied as the calculation tide pattern, and the diffusion, transportation, and dilution process of the conservative material in the calculation water area are obtained continuously. Figure 6 shows the distribution of conservative materials at different times over three months. Note that the concentration value of conservative substances on each grid point not only represents its own concentration, but also is an important indicator of local water exchange degree. The period of the water exchange rate reaching 95% is about 60 days. Figure 8d,e shows that the trend of concentration distribution and isoline trend in the bay are close, while the overall concentration decreases and the concentration contour continues to be extrapolated. After one and a half months, the exchange ratio of all water bodies in the bay reaches more than 85%; after two months, the exchange ratio of most water bodies in the bay reaches more than 90%, except for some waters at the top of the west of the Bay. It can be considered that the water exchange in Sanmen Bay has been basically completed at this time.

**Figure 6.** Water semi-exchange time (**a**) and 95% water exchange time (**b**). **Figure 6.** Water semi-exchange time (**a**) and 95% water exchange time (**b**).

port in the bay head has dropped below 0.1 unit. Figure 8d,e shows that the trend of concentration distribution and isoline trend in the bay are close, while the overall concentration decreases and the concentration contour continues to be extrapolated. After one and a half months, the exchange ratio of all water bodies in the bay reaches more than 85%; after two months, the exchange ratio of most water bodies in the bay reaches more than 90%, except for some waters at the top of the west of the Bay. It can be considered that the water exchange in Sanmen Bay has been After five days (Figure 7a), the water exchange degree of different regions in the bay is quite different. On the whole, the concentration of conservative material decreased gradually from the top of the bay to the estuary, indicating an increased exchange degree from the bay head to the bay mouth. At the same time, the water exchange degree of the bay mouth section increased gradually from the west to the east part of the bay. The direction of concentration isoline near the bay mouth was NNE-SSW, and the water exchange rate reached more than 90% on the fifth day in the bay mouth. The water exchange capacity of

port in the bay head has dropped below 0.1 unit.

port in the bay head has dropped below 0.1 unit.

port in the bay head has dropped below 0.1 unit.

continues to be extrapolated. After one and a half months, the exchange ratio of all water bodies in the bay reaches more than 85%; after two months, the exchange ratio of most water bodies in the bay reaches more than 90%, except for some waters at the top of the west of the Bay. It can be considered that the water exchange in Sanmen Bay has been

Figure 8d,e shows that the trend of concentration distribution and isoline trend in the bay are close, while the overall concentration decreases and the concentration contour continues to be extrapolated. After one and a half months, the exchange ratio of all water bodies in the bay reaches more than 85%; after two months, the exchange ratio of most water bodies in the bay reaches more than 90%, except for some waters at the top of the west of the Bay. It can be considered that the water exchange in Sanmen Bay has been

Figure 8d,e shows that the trend of concentration distribution and isoline trend in the bay are close, while the overall concentration decreases and the concentration contour

basically completed at this time.

basically completed at this time.

basically completed at this time.

Shipu port is relatively strong, and the water exchange rate from the bay head to the bay mouth rises from 40% to about 80%.

**Figure 7.** Conserved matter distribution after 5 days (**a**), 15 days (**b**), 30 days (**c**), 45 days (**d**) and 60 days (**e**).

Half a month later, most of the water areas in the bay that had not been exchanged five days ago have been exchanged to a certain extent, and the concentration value has dropped to less than 0.9 units.

One month later, except for the small tidal flats with high elevation in Xiaodao, most of the water bodies in Sanmen Bay have completed semi exchange, and the water exchange rate in the Bay has basically reached more than 60%. To facilitate the observation of the concentration distribution in the bay, the upper limit of concentration in the figure is changed to 0.4 units. The concentration isolines at the top and mouth of the bay continue to move into the bay, and the concentration gradient is significantly reduced. The overall distribution trend of the water exchange degree is still similar to that before. The concentration contour line in the western part of the bay is roughly along the NE-SW direction, and the relatively high concentration waters are mainly located in Qimen port and Haiyou harbor, with a concentration value of between 0.25 and 0.35. The concentration of Shipu port in the bay head has dropped below 0.1 unit.

Figure 8d,e shows that the trend of concentration distribution and isoline trend in the bay are close, while the overall concentration decreases and the concentration contour continues to be extrapolated. After one and a half months, the exchange ratio of all water bodies in the bay reaches more than 85%; after two months, the exchange ratio of most water bodies in the bay reaches more than 90%, except for some waters at the top of the west of the Bay. It can be considered that the water exchange in Sanmen Bay has been basically completed at this time.

port in the bay head has dropped below 0.1 unit.

water bodies in the bay reaches more than 90%, except for some waters at the top of the west of the Bay. It can be considered that the water exchange in Sanmen Bay has been

bay are close, while the overall concentration decreases and the concentration contour continues to be extrapolated. After one and a half months, the exchange ratio of all water bodies in the bay reaches more than 85%; after two months, the exchange ratio of most water bodies in the bay reaches more than 90%, except for some waters at the top of the west of the Bay. It can be considered that the water exchange in Sanmen Bay has been

Figure 8d,e shows that the trend of concentration distribution and isoline trend in the

**Figure 8.** Tidal prism changing process (28 November 2009 to 12 December 2009). **Figure 8.** Tidal prism changing process (28 November 2009 to 12 December 2009).

#### 3.3.2. Water Exchange Ability

basically completed at this time.

basically completed at this time.

3.3.2. Water Exchange Ability Tidal prism means the volume of tidal water that a certain bay can hold. It is an important indicator of the environmental assessment of a bay and an important parameter reflecting the exchange of sea water in the bay. The amount of tidal prism is of great significance to the marine environment, the exchange of water bodies in the bay, the maintenance of the port branch, and the water depth in the channel. Sanmen Bay is a typical semi-enclosed bay, the rivers flowing into the bay is mountainous rivers. Therefore, when calculating the tidal volume of Sanmnen Bay, the tidal volume flowing out of the coastal Tidal prism means the volume of tidal water that a certain bay can hold. It is an important indicator of the environmental assessment of a bay and an important parameter reflecting the exchange of sea water in the bay. The amount of tidal prism is of great significance to the marine environment, the exchange of water bodies in the bay, the maintenance of the port branch, and the water depth in the channel. Sanmen Bay is a typical semi-enclosed bay, the rivers flowing into the bay is mountainous rivers. Therefore, when calculating the tidal volume of Sanmnen Bay, the tidal volume flowing out of the coastal estuary from the calculation area is ignored, and only the part in Sanmen Bay is considered. Two tidal current channel sections between the bay and the open sea, the Sanmen Bay section and Shipu Port are perpendicular to the longitudinal axis of the main waterway and Shipu section (Figure 8).

estuary from the calculation area is ignored, and only the part in Sanmen Bay is considered. Two tidal current channel sections between the bay and the open sea, the Sanmen Bay section and Shipu Port are perpendicular to the longitudinal axis of the main water-The tidal volume is defined as the newly added tidal volume entering the bay from the low tide time to the high tide time in any one tide cycle. The tidal volume of a tidal cycle can be expressed as:

$$Q = \int\_{T\_{\rm low}}^{T\_{\rm high}} \int\_{A\_1} \mathcal{U}\_1 D\_1 dA\_1 dt + \int\_{T\_{\rm low}}^{T\_{\rm high}} \int\_{A\_2} \mathcal{U}\_2 D\_2 dA\_2 dt \tag{5}$$

of semi exchange capacity in Sanmen Bay varies greatly in different regions of the bay. Generally speaking, the water exchange capacity of the bay mouth and Shipu port is strong, and the water exchange in the west of the bay is relatively slow compared with that in the East. On the whole, the half exchange time of water in Sanmen Bay is less than

(5)

.

the low tide time to the high tide time in any one tide cycle. The tidal volume of a tidal cycle can be expressed as: ℎℎ ℎℎ The hydrodynamic model is ideal for the simulation results of regional tides and tidal current processes. The simulated flow field can basically reflect the calculation of regional hydrodynamics. The calculation results can be used as the basis for the study of water exchange and water environment capacity in Sanmen Bay.

 = ∫ ∫ 111 1 + ∫ ∫ 222 2 The tidal volume of Sanmen Bay is relatively large. It's between <sup>15</sup> <sup>×</sup> <sup>10</sup><sup>8</sup> <sup>∼</sup> <sup>30</sup> <sup>×</sup> <sup>10</sup>8m<sup>3</sup> during a spring-neap tidal cycle, <sup>20</sup> <sup>×</sup> <sup>10</sup><sup>8</sup> <sup>∼</sup> <sup>30</sup> <sup>×</sup> <sup>10</sup>8m<sup>3</sup> during spring tides, and <sup>15</sup> <sup>×</sup> <sup>10</sup><sup>8</sup> <sup>∼</sup> <sup>18</sup> <sup>×</sup> <sup>10</sup>8m<sup>3</sup> during neap tides. The average tidal prism is about 20.78 <sup>×</sup> <sup>10</sup>8m<sup>3</sup> .

The hydrodynamic model is ideal for the simulation results of regional tides and tidal current processes. The simulated flow field can basically reflect the calculation of regional hydrodynamics. The calculation results can be used as the basis for the study of water exchange and water environment capacity in Sanmen Bay. The tidal volume of Sanmen Bay is relatively large. It's between 15 × 108~30 × 108m<sup>3</sup> during a spring-neap tidal cycle, 20 × 108~30 × 108m<sup>3</sup> during spring tides, and 15 × 108~18 × 108m<sup>3</sup> during neap tides. The average tidal prism is about 20.78 × 108m<sup>3</sup> According to the results of numerical calculation of water exchange, the distribution According to the results of numerical calculation of water exchange, the distribution of semi exchange capacity in Sanmen Bay varies greatly in different regions of the bay. Generally speaking, the water exchange capacity of the bay mouth and Shipu port is strong, and the water exchange in the west of the bay is relatively slow compared with that in the East. On the whole, the half exchange time of water in Sanmen Bay is less than 23 days, and 95% of the water exchange period is within 50 days in relatively open main water area; the half exchange time of water body in most areas of the branches is more than 10 days, and 95% of the water exchange period is more than 50 days; the water exchange time of the west end of Shipu port is longer than that of the east end, the half exchange period is less than 8 days, and 95% of the water exchange period is less than 40 days.

## **4. Discussion**

#### *4.1. Estimation of Environmental Capacity*

Based on the precondition that to maintain the function of the environmental capacity of water, pollutant emission maximum that receiving waterbody can endure, that is to say, are permissible quantity of pollutants under the goal of water quality and hydrological condition. According to the situation of the water environment in Sanmen Bay, to calculate environment capacity about CODMn is to figure out the maximum value of emissions' sum from pollution loads at all outfalls. Gaining value which is as great as possible on environment capacity is important. Yet important management methods for contaminants controlling and environment protection might coordinate with the operability of management.

Working out a linear programming problem is to figure out a linear function's maximum or minimum under the constraint of a set of linear equations or inequations.

The response coefficient method for environment capacity calculation transforms into a linear programming maximization problem [12]. It means:

Object function:

$$\max \sum\_{j=1}^{n} \mathcal{Q}\_{j} \tag{6}$$

Constraint equation:

$$\begin{aligned} \mathcal{C}\_{0i} + \sum\_{j=1}^{n} \mathfrak{a}\_{ij} Q\_j &\le \mathcal{C}\_{\text{si}} \, (i = 1, 2, \dots, m) \\ Q\_j &\ge 0, \, (j = 1, 2, \dots, n) \end{aligned} \tag{7}$$

where, *j* means pollutant sources' serial number, *n* means the number of sources; *i* means the serial number of control points of water quality, *m* means the number of control points of water quality; *C*0*<sup>i</sup>* means background concentration of control points; *αai* means the coefficient of the *j*th pollution source's emission at the *i*th control points of water quality.

To quickly obtain the maximum value, the problem was transformed into the standard forms in linear programming. Let *C<sup>i</sup>* = *Csi* − *C*0*<sup>i</sup>* , to convert the inequation into an equivalent equation.

Object function:

$$\max Q = \sum\_{j=1}^{n} Q\_j \tag{8}$$

Constraint equation:

$$\sum\_{j=1}^{n} \alpha\_{i\bar{j}} Q\_{\bar{j}} \le \mathbb{C}\_{i\prime} \ (i = 1, 2, \dots, m) \tag{9}$$

$$Q\_j \ge 0, \ (j = 1, 2, \dots, n) \tag{10}$$

where, *C<sup>i</sup>* means the *i*th concentration capacity of the control points of water quality. Environment capacity assessment in this study involved COD, labile phosphate, and inorganic nitrogen. Control stations distribution can be seen in Figure 1d.

#### 4.1.1. The Responses Factor Field of COD

According to the method of response factor, the response factor field of pollution source in each catchment unit needs to be calculated first. The response factor field uses the same region and mesh as the pollution diffusion model. The initial condition was set as 0 to exclude other source strength's influence. The concentration field (also known as response factor field) is as Table 4 shows.


**Table 4.** CODMn concentration field (mg/L).
