Network Analysis of Ship Domestic Sewage Discharge—The Yangtze River Case

Abstract

Water transportation has always occupied a large proportion of China’s transportation and has become the key to China’s economic development. Water transportation is called “green transportation” in the industry due to the advantages of low transportation cost, high safety factor, and large capacity. However, water transportation has caused a great impact on the ecological environment of the waters for a long time, and solving the problem of sewage pollution from ships has also become an unavoidable problem. To control pollution from ships, it is essential to analyze the characteristics of ship domestic sewage discharge. In this study, a ship domestic sewage discharge complex network (SDCN) is established based on the ship voyage data to analyze the discharge characteristics in the Yangtze River. According to the topological analysis, the SDCN is a small-world network with the power-law degree distribution and superliner betweenness-degree correlation as distinguishing characteristics. The top five MDs with the highest in-vertex strength are Chaotianmen MD (S = 165,129,561), Tongling MD (S = 66,426,616), Maanshan MD (S = 62,087,158), Baqu MD (S = 59,964,550), and Shashi MD (S = 55,569,399), which indicates that these MDs receive a large amount of sewage. And the volume of domestic sewage between Chaotianmen MD and Baqu MD is the largest. The results can help us understand the discharge characteristics of ship domestic sewage and how they can be targeted to develop control measures for the countermeasures of “zero discharge” for inland ships.

1. Introduction

A significant amount of international transportation trade is made up of water transportation, which successfully ensures the coordinated growth of national and regional economies [1]. In recent years, along with the development of the shipping trade industry, it also poses a huge challenge to prevent water ecological environment pollution, and ship discharge of domestic sewage is one of the main sources of water pollution [2]. Domestic sewage is the drainage from dishwater, shower, laundry, bath, and washbasin drains. The discharge of domestic sewage is not regulated by the International Maritime Organization (IMO). But in addition to bacteria and organic matter, the presence of nutrients (nitrogen and phosphorous) and contaminants (chemicals present in places they should not be or in higher concentrations than if they had occurred naturally) that can cause eutrophication could also pose a threat to the environment [3,4]. Depending on the activities conducted on board each ship specifically, the quantity and makeup of the household sewage varies. Large cruise ships offer amenities that are comparable to those found in land-based hotel resorts, including kitchens, swimming pools, hair salons, dry cleaning, and restaurants [5]. Chemicals are frequently used for normal maintenance (such as cleaning pipes and water) and passenger services [6,7]. Previous research has indicated that domestic sewage contains metals in piping and wastewater treatment, preservatives and antibacterial agents discharged from personal care goods from shower and washing water, detergents and other chemicals in dish water, and more [8]. The International Maritime Organization developed the International Convention for the Prevention of Pollution from Ships (MARPOL) to reduce the marine pollution from pollutants released during ship operations. China developed and implemented the Effluent Standard for Pollutants from Ships (GB 3552-83) [9,10]. This standard sets down the maximum concentration of oily water and sewage that can be discharged, along with rules for rubbish disposal. The most recent version of the standard, known as the Discharge Standard for Water Pollutants from Ships (GB 3552-2018), lays out the guidelines for controlling the discharge of sewage, oily water, waste containing toxic liquids, and ship waste into environmental water bodies [11]. It also outlines the requirements for the standard’s implementation and oversight. Ship domestic sewage in inland navigable waters should be released into receiving facilities following temporary storage on board or following treatment by ship-borne sewage treatment facilities that follow standard operating protocols.

The regulatory work has been partially neglected when it comes to the direct dumping of various ship wastewaters into the sea. For instance, after a ship sails a certain distance from the coast, it is still legal to dump raw sewage into the ocean. Regarding sewage discharge and nutrient content, the Baltic Sea is currently the only special area under MARPOL Annex IV that has been defined. In this region, the sewage from passenger ships must either be delivered in port or treated following the IMO guidelines found in MEPC. 227(64) [8]. The rules will be implemented for all passenger ships starting in 2021 and for newly constructed passenger ships starting in 2019. The deadline for direct travel from St. Petersburg, Russia, to the North Sea has been extended to 1 June 2023. Certain geographical regions are subject to national regulations; for example, the Norwegian Maritime Authority has banned the release of graywater from ships certified to carry over 100 people, with a gross tonnage of 2500 or more in the world heritage fjords [12]. The US Environmental Protection Agency’s (USEPA) Vessel General Permit governs graywater discharge in the country and is based on the location and kind of vessel [13]. Currently, a lot of research is being carried out to analyze the environmental impact of domestic sewage from ships and ship domestic sewage treatment [14,15,16,17]. However, studies that quantify the waste produced by ships and the distribution characteristics of the ship domestic sewage are relatively less in the Yangtze River. GIS-based technology has been utilized to investigate the spatial distribution features of fine ship sewage production in the lower portions of the Yangtze River, from Nanjing to the estuary [18]. In 2022, to further protect the water environment of the Yangtze River and promote the high-quality development of Yangtze River shipping, zero discharge of water pollutants from ships has been comprehensively promoted in the Anhui and above sections of the Yangtze River trunk line. Ships have been encouraged to adopt the “zero-discharge” disposal method of “on-board storage and on-shore discharge” to treat domestic sewage. Sewage discharge lines other than dedicated lines shall be removed. Therefore, it would be a very meaningful research topic to analyze the characteristics of ship domestic sewage discharge based on the port of departure and port of destination.

A comparison between the proposed method in this study and other methods can be seen in

Table 1. A comparison between the proposed method in this study and other methods.

Research	Research Topic
	Estimation of Ship Domestic Sewage	Environmental Impact	Spatial Distribution Characteristics	Discharge Characteristics of Different Ship Types	Reception Characteristics of Different Port
Maljutenko et al., 2020 [16]	X		X
Yteberg et al., 2020 [15]	X	X
Jalkanen et al., 2020 [14]	X		X
Parks et al., 2019 [17]	X		X
Chen et al., 2022 [18]	X		X
Proposed method in this study	X		X	X	X

.

In this study, we build a ship domestic sewage complex network (SDCN), where nodes indicate maritime departments (MDs) with ports and edges denote connections determined by routes between MDs, in order to analyze the discharge characteristics of ship domestic sewage in the Yangtze River. We can better comprehend the spatial relationships and functions of various MDs by looking at the structure of the SDCN.

The remainder of this paper is structured as follows. Section 2 explains how the model is constructed. Section 3 is a case study to demonstrate the characteristics of the ship domestic sewage in the Yangtze River. Discussion is provided in Section 4, and the conclusion is provided in Section 5.

2. Methodology

The overall steps for this study can be divided into data preparation and modeling and analyzing the SDCN, and the configuration figure can be seen in Figure 1.

2.1. Modeling Ship Sewage Discharge Characteristic Network

Complex networks theory has been widely applied in the sector of transportation [19,20,21,22,23,24]. Maritime transportation most commonly uses global transportation networks, where ship routes and ports are considered edges and nodes, respectively, according to complex network theory [25]. The purpose of the transportation network is to investigate worldwide transportation systems; however, the ship domestic sewage discharge complex network (SDCN) has been set up specifically to investigate the Yangtze River’s ship domestic sewage discharge characteristics.

2.1.1. Determination of Edges

We must first ascertain the ships’ ports of origin and destination before we can build a port network on the Yangtze River. The Yangtze River maritime department is modeled as the node of the SDCN because the maritime department (MD) regulates ship domestic sewage in the port. Additionally, if a ship exists that originates at the port in an MD jurisdiction represented by the first node and ends at the port in an MD jurisdiction represented by the second node, we create an edge connecting the two nodes. In addition, since the ship route is directional, the ship sewage discharge characteristic network is directed.

2.1.2. Determination of Weights

In this study, we introduced the domestic sewage estimation method to determine the weight of edges in the SDCN. The total sewage discharge between a pair of MDs is mapped as the edge weight. Firstly, the research dataset used to estimate the generation of ship domestic sewage is obtained from Automatic Identification System (AIS) data, ship inbound and outbound reports, ship static information statistical tables, domestic and foreign research reports, etc. The calculation formula of the generation of ship domestic sewage is as follows:

$$T_{i,j}^{ds}={\displaystyle \sum A_{i,j}\cdot r_{i,j}\cdot q_{i,j}}$$

(1)

In Equation (1), $T_{i,j}^{ds}$ is the generation of domestic sewage by ship i in route j, $A_{i,j}$ is the sailing time of ship i in route j, $r_i$ is the number of crew and passengers on ship i in route j, $q_i$ is the coefficient of ship domestic sewage generation of ship i in route j. As shown in

Table 2. The coefficient from different ship types.

Ship Type	Coefficient (L/person/day)
Oil and chemical tankers	105
Cargo ships	119
Passenger ships	157
Fishing ships	222
Offshore ships	153

, the coefficient is determined by different ship types [26,27].

The total domestic sewage generation in route j can be calculated as follows:

$$T_j^{ds}={\displaystyle \sum T_{i,j}^{ds}}$$

(2)

where the $T_j^{ds}$ is the total domestic sewage generation in route j. Route is represented by the edge in the ship sewage discharge characteristic network, and the weight of the edge is represented by $T_{}^{ds}$.

2.2. Measurements in Complex Network Analysis

Some variables often employed in complex network analyses, such as the cumulative degree distribution, vertex strength, average path length, clustering coefficient, and betweenness centrality, are selected in order to study the overall network structure of the SDCN [28,29]. An adjacency matrix $A(N\times N)$ can be used to describe the SDCN, $a_{ij}=1$ represent the MD i and MD j, which are an origin–destination pair. Otherwise, $a_{ij}=0$. $N$ is the amount of nodes in the SDCN.

(1)

Cumulative degree distribution

The number of edges that node i connects is represented by its degree. The degree can be calculated as follows:

$$k_i={\displaystyle \sum _{j=0}^N{a}_{ij}}$$

(3)

A frequent method to represent a node’s connectedness inside a network is through the concept of degree. More MDs are easily accessed in the analysis network at higher degrees.

In the SDCN, the likelihood of arbitrarily choosing a node with a degree of at least k is expressed by the cumulative degree distribution. The calculation method is given by:

$$P(k)={\displaystyle \sum _{k^{\prime }=k}^{\infty }p(k^{\prime })}$$

(4)

The cumulative degree distribution is a crucial characteristic that can be used to identify a wide range of network phenomena in real transportation systems, including traffic flow spread and network robustness.

(2)

Vertex strength

The total of a node’s edge weights is known as the vertex strength. The definition of the average vertex strength is as follows:

$$S_i={\displaystyle \sum _{j\in N_i}{w}_{ij}}$$

(5)

$$\overline{S}=\frac{1}{N}{\displaystyle \sum _{i=1}^N{S}_i}$$

(6)

where $\overline{S}$ represents the average vertex strength of a network, $S_i$ represents the vertex strength of node i, $w_{ij}$ represents the weight of the edge between node i and node j, $N_i$ represents the set of adjacent points of node i.

(3)

Average path length

The following formula is used to determine the average path length, which indicates the average minimum number of edges between an arbitrarily chosen node pair in the SDCN.

$$L=\frac{1}{\frac{1}{2}N(N-1)}{\displaystyle \sum _{i\ge j}{d}_{ij}}$$

(7)

where $d_{ij}$ is the fewest number of edges that connect nodes i to j.

(4)

Clustering coefficient

The clustering coefficient measures the degree to which nodes in a graph tend to cluster together. In real-world networks, nodes tend to create tightly knit groups characterized by a relatively high density of ties. The definitions of the clustering coefficient are provided by the following equation:

$$C_i=\frac{E_i}{C_{k_i}^2}$$

(8)

where $C_i$ represents the local clustering coefficient of node $i$, $E_i$ represents the number of connections among node $i^{\prime }\mathrm{s}$ neighbors that are actually realized, $C_{k_i}^2$ represents the number of all possible connections among node $i^{\prime }\mathrm{s}$ neighbors.

(5)

Betweenness centrality

Betweenness centrality measures the extent to which a node controls the shortest pathways of all node pairs and is often used to depict transitivity in transportation networks [30]. The greater $B_i$, the more crucial the function of transfer MD i. Node i’s betweenness is defined as the proportion of all shortest routes going through it:

$$B_i={\displaystyle \sum _{s\ne i\ne t}\frac{n_{st}^i}{g_{st}}}$$

(9)

where $g_{st}$ represents the number of shortest paths from node s to node t, and $n_{st}$ represents the number of shortest paths in $g_{st}$ that pass through node i.

3. Case Study

3.1. Research Area and Data

The greatest river that traverses both east and west China is the Yangtze River, commonly known as the “golden waterway”. It has been the main channel for travel and commercial trade [31]. The river has seen siltation, loss of wetlands and lakes, industrial pollution, plastic pollution, agricultural runoff, and other issues in recent years that make seasonal floods worse. More people are becoming aware of the conflict between the growth of shipping and the preservation of the environment. To ensure coordinated pollution prevention and control countermeasures, it is therefore necessary to compute the amount of ship water pollutants and analyze the discharge characteristics of ship domestic sewage. This will aid in decision-making for the ship and management department. The research region in this study is the Yangtze River, which runs from Sichuan to Anhui, as Figure 2 illustrates. As the primary region for environmental preservation along the Yangtze River, this portion has grown in importance. So, the Yangtze River’s stretches from Sichuan to Anhui are included in this study’s geographical scope.

In recent years, ship voyage data have proved to be a valuable tool to investigate ship navigation and pollution. The research data in this study are ship voyage data. Currently, ships are obligated by the maritime department to submit the voyage information, including ship name, ship type, maritime department of departure, departure time, maritime department of destination, arrival time, number of crew members, etc.

The vessel voyage data in the Yangtze River in 2019 have been used in this study. It should be noted that ships operating in the port have not been considered in this study. These data were provided by the Changjiang River Administration of Navigational Affairs, which is under the Ministry of transport in China. A portion of research data are shown in

Table A1. A portion of research data in this study.

Ship Name	Ship Type	MD of Departure	Departure Time	MD of Destination	Arrival Time	Number of Crew Members
Xinchangjiang06029	Bulk Ship	Chongqing Wanzhou MD	31 January 2019 23:55	Yueyang Linxiang MD	8 February 2019 20:30	10
Ninghuayun2	LNG ship	Yueyang Linxiang MD	31 January 2019 23:50	Wuhan Yangluo MD	4 February 2019 9:53	12
Eshi2197	Oil tanker	Wuhan Qingshan MD	31 January 2019 23:20	Chongqing Fuling MD	14 February 2019 6:46	10
Changxing69	Bulk ship	Wuxue MD	1 December 2019 0:39	Fuchi MD	7 December 2019 21:14	7
Huayingshan	Ro-Ro passenger ship	Chaotianmen MD	1 December 2019 0:59	Baqu MD	2 December 2019 15:10	88

in Appendix A.

We first ascertain the origin and destination MDs of the ships in the dataset in order to build an SDCN model. All MDs in the research area can be mapped as nodes in the SDCN and connected by determining the starting MD and ending MD in our investigation. As a result, these 63 MDs are part of our analytic network;

Table A2. Maritime departments in this study.

No.	MD	No.	MD	No.	MD	No.	MD
1	Cuiping	17	Yunyang	33	Huarong	49	Jiujiang Xingang
2	Nanxi	18	Fengjie	34	Linxiang	50	Hukou
3	Jiangan	19	Wushan	35	Xintan	51	Pengze
4	Naxi	20	Badong	36	Xianning	52	Huayang
5	Jiangyang	21	Guizhou	37	Jinkou	53	Dongliu
6	Hejiang	22	Baqu	38	Zhuankou	54	AnqingGangqu
7	Yongchuan	23	Gezhouba	39	Wuhan Gangqu	55	Niutoushan
8	Jiangjin	24	Yidu	40	Qingshan	56	Congyang
9	Banan	25	Zhijiang	41	Yangluo	57	Chizhou
10	Chaotianmen	26	Gongan	42	Erzhou	58	Tongling
11	Changshu	27	Shashi	43	Huanggang	59	Digang
12	Fuling	28	Jiangling	44	Huangshi Gangqu	60	Yuxikou
13	Fengdu	29	Shishou	45	Jinchun	61	Wuhu Gangqu
14	Zhongxian	30	Jianli	46	Fuchi	62	Cihu
15	Shizhu	31	Honghu	47	Wuxue	63	Maanshan
16	Wanzhou	32	Chenglingji	48	Jiujiang Gangqu

in Appendix A contains the details of the MDs in this study. The number of ships entering the MD and leaving the MD can be seen in

Table A3. Number of ships entering the MD.

No.	Number of Ships	No.	Number of Ships	No.	Number of Ships	No.	Number of Ships
1	1384	17	1801	33	67	49	1595
2	1492	18	5018	34	4285	50	4054
3	2406	19	3381	35	479	51	2523
4	1875	20	1592	36	2624	52	2221
5	4731	21	388	37	1943	53	1062
6	1907	22	8711	38	3426	54	4315
7	3327	23	1244	39	1551	55	6099
8	3975	24	8155	40	6386	56	2420
9	7398	25	4784	41	8291	57	2830
10	22,733	26	1106	42	2938	58	10,581
11	7334	27	8442	43	2117	59	6637
12	9706	28	865	44	3697	60	1640
13	8678	29	780	45	3212	61	6079
14	5265	30	982	46	7835	62	2855
15	2871	31	423	47	4704	63	7215
16	8998	32	6253	48	4252

and

Table A4. Number of ships leaving the MD.

No.	Number of Ships	No.	Number of Ships	No.	Number of Ships	No.	Number of Ships
1	1375	17	1761	33	66	49	1597
2	1482	18	5044	34	4444	50	3960
3	2439	19	3383	35	476	51	2656
4	1857	20	1599	36	2549	52	2234
5	4693	21	370	37	1937	53	1055
6	1896	22	8632	38	3522	54	4291
7	3331	23	1234	39	1533	55	6380
8	3991	24	8060	40	6417	56	2414
9	7433	25	4813	41	8243	57	2867
10	22,771	26	1085	42	2976	58	10,398
11	7290	27	8410	43	2124	59	6384
12	9680	28	887	44	3652	60	1709
13	8680	29	802	45	3166	61	6226
14	5278	30	972	46	7740	62	2943
15	2868	31	409	47	4589	63	7441
16	9090	32	6082	48	4249

in Appendix A, respectively. There are 63 nodes and 3110 edges in the SDCN model in the Yangtze River. It should be noted that there are no isolated nodes in the networks, which means that in the spatial correlation network, there are no variables that are not related to each other.

3.2. Topological Properties in SDCN

Table 3. Basic network parameters of SDCN.

Nodes	Edges	Average In-Degree	Average Out-Degree	Average Shortest Path Length	Diameter	Average Cluster Coefficient
63	3110	45.07	45.07	1.34	3	0.796

lists the SDCN’s fundamental topological characteristics. About 45.07 is the average in-degree for the SDCN. The top five MDs with the highest in-degree, i.e., Chaotianmen MD (67), Shashi MD (66), Yidu MD (66), Chenglingji MD (66), and Fuling MD (64) are shown in Figure 3. The average out-degree of the SDCN is 46.043. The top five MDs with the highest out-degree are Fuling MD (65), Chaotianmen MD (64), Shashi MD (64), Yidu MD (64), and Wanzhou MD (62). The degree represents the traffic volume of the port in the MD.

The diameter is 3 and the average shortest path length is 1.34. The network’s average cluster coefficient is 0.796. The SDCN may be considered a small-world network because of its low average path length and strong clustering coefficient. Upon computing the minimum travel lengths for every pair of MDs (i.e., (63 − 62)/2 pairings), we see that over 80% of the routes consist of no more than two transfers.

Table 4. Distribution of the shortest path length of SDCN.

Shortest Path	Number of Paths	Percentage of Paths	Number of Transfers
1	298	15.26%	0
2	578	29.59%	1
3	922	47.20%	2
4	155	7.95%	3

offers a comprehensive view of the SDCN’s shortest path.

The specifics of the distributions and relationships of a few topological features are displayed, as seen in Figure 4.

The degree distribution reveals how the SDCN is set up and how it has become essential to network analysis. The SDCN displays a power-law degree distribution, as seen in Figure 4a. For the directed SDCN, the cumulative in-degree distribution p(k_in) and cumulative out-degree distribution p(k_out) are almost the same as the p(k) in the undirected network. The correlation between in-degree k_in and out-degree k_out can be seen in Figure 4b. The strong correlation between k_in and k_out shows that the SDCN is a symmetrical network. It means that there is a high probability that a ship exists from MD j to MD i if there is a ship from MD i to MD j. To assess the nodes’ significance in the SDCN’s transitivity, the correlation between the degree and betweenness has been computed. Figure 4c illustrates how high-degree nodes could have to handle additional transfer occupations. The association between the degree and clustering coefficient is seen in Figure 4d. We discover that while the connections between the high-degree MDs in the SDCN are dense, several low-degree MDs are not fully linked. Thus, the clustering coefficients of the low-degree nodes are larger.

The SDCN is a small-world network with particular characteristics of a power-law degree distribution and a superliner betweenness-degree correlation, according to the results of the topological study.

3.3. Ship Domestic Sewage Discharge Characteristics in SDCN

Ship domestic sewage in the SDCN has been investigated in this section. The section can be divided into two parts, the ship domestic sewage volume of output and ship domestic sewage volume of input. Based on the research data provided by the Changjiang River Administration, the SDCN can be visualized via Gephi software 0.9.2 which developed by Mathieu Jacomy, a researcher at the Paris Institute of Political Science in 2006. The size of the nodes corresponds to their vertex strength, as seen in Figure 5. Figure 5a depicts the in-vertex strength of the node in the SDCN and the in-vertex strength represents the domestic sewage volume of input in an MD. Figure 5b depicts the out-vertex strength of the node in the SDCN and the out-vertex strength represents the domestic sewage volume of output in an MD.

Firstly, the characteristic of in-vertex strength has been researched. The top five MDs with the highest in-vertex strength are Chaotianmen MD (S = 165,129,561), Tongling MD (S = 66,426,616), Maanshan MD (S = 62,087,158), Baqu MD (S = 59,964,550), and Shashi MD (S = 55,569,399). This indicates that these MDs receive a large amount of sewage. Strong sewage reception, transportation, and treatment capabilities are required in the ports of these MDs. The proportion of different ship types and the total volume of input domestic sewage can be seen in Figure 6, with a large proportion of cargo ships (bulk ships and dry cargo ships) in Chaotianmen MD, Tongling MD, and Maanshan MD. Therefore, domestic sewage is generated by these ships. In Baqu MD, cruise ships, Ro-Ro passenger ships, and passenger ships account for a larger rate. Notably, the volume of domestic sewage of passenger ships is higher than that of cargo ships with equal amounts of passenger ships and cargo ships. A large number of passengers on board is the main reason. The top five MDs with the highest out-vertex strength are Tongling MD (S = 88,276,594), Chaotianmen MD (S = 165,129,561), Fengdu MD (S = 165,129,561), Digang MD (S = 23,509,156), and Fuchi MD (S = 45,275,557). The largest number of ships departing from Tongling MD are chemical ships, and cargo ships account for a larger rate in the other four MDs. A special feature emerges in Chaotianmen MD. Due to the large number of passengers and long voyage of the cruise ship, the largest proportion of number of ships is bulk ships, but cruise ships contribute the largest proportion of the volume of ship domestic sewage. The proportion of different ship types and the total volume of output domestic sewage can be seen in Figure 7.

After describing the pattern of ship domestic sewage in the SDCN, we further analyze the ship domestic sewage distributions and relationships with the topology in Figure 8.

The cumulative distribution of the node vertex strengths is displayed in Figure 8a. We discover that the distribution is power-law distributed, which is typically in line with Figure 4a. The correlation between the degree and vertex strength in Figure 8b indicates that more ship domestic sewage may pass through a particular node if its connectivity is stronger. The edge weight p(w) can be seen in Figure 8c. Because the p(w) has a power-law distribution, some edges produce a lot of domestic sewage while the majority of edges have fewer trips. Figure 8d shows the link between the edge weight w_ij and the degrees of nodes i and j that are connected by that edge. The vertex strength between two nodes can be seen in Figure 9. The size of the edges represents the proportion to the volume of ship domestic sewage between two MDs. Here, a few unique characteristics become apparent. Several edges have a low k_ik_j but high domestic sewage (red nodes in Figure 8d), like Baqu MD–Chaotianmen MD and Chaotianmen MD–Baqu MD, while several edges with a high k_ik_j only experience low domestic sewage, like Chaotianmen MD–Fuling MD and Fuling MD–Chaotianmen MD (green nodes in Figure 8d).

The traffic volume features can be seen from the edge sizes shown in Figure 9; the size of the edges represents the number of ships between two MDs. It can be seen from Figure 9 that the size of the edge between Chaotianmen MD and Fuling MD is the largest, but the volume of ship domestic sewage is not very large (Figure 8d). Different ship types between Chaotianmen MD and Fuling MD can be seen in Figure 10. In Figure 10a, from Chaotianmen MD to Fuling MD, the number of multipurpose ships accounted for the largest, followed by chemical ships, bulk ships, container ships, oil tankers, etc. In Figure 10b, from Fuling MD to Chaotianmen MD, the number of oil tankers accounted for the largest, followed by chemical ships, dry cargo ships, multipurpose ships, container ships, etc. Despite the large number of ships between Chaotianmen MD and Fuling MD, the amount of sewage generated is not significant due to the small number of crew members.

The ship domestic sewage features can be seen from the edge sizes shown in Figure 11; the size of the edges represents the volume of domestic sewage between two MDs. It can be seen from Figure 11 that the size of the edge between Chaotianmen MD and Baqu MD is the largest. Different ship types between Chaotianmen MD and Baqu MD can be seen in Figure 12. In Figure 12a, from Chaotianmen MD to Baqu MD, the number of Ro-Ro passenger ships accounted for the largest, followed by cruise ships, passenger ships, bulk ships, etc. In Figure 12b, from Baqu MD to Chaotianmen MD, the number of Ro-Ro passengers accounted for the largest, followed by cruise ships, bulk ships, passenger ships, etc. Most of the ships between Chaotianmen MD and Baqu MD are passenger ships, and there are many passengers on board, resulting in a large amount of sewage being generated.

4. Discussion and Conclusions

4.1. Limitations and Future Improvements

This work has introduced a method of network science to analyze the discharge characteristics of ship domestic sewage in the Yangtze River by constructing a ship domestic sewage complex network (SDCN), where nodes represent maritime departments (MDs) with ports and edges denote connections defined by routes between MDs. Although the results of the case studies and empirical findings are promising, several factors could further improve the proposed method and strengthen the findings and future applicability.

(i)

Optimize the coefficient of ship type in the domestic sewage estimation method. In this study, the ship domestic sewage generation coefficient of different ship types is based on existing research, including oil and chemical tankers, cargo ships, passenger ships, fishing ships, and offshore ships. However, the number of ship types in the Yangtze River is far greater than that. So, the coefficient of ship type in the estimation method should be more accurately determined.

(ii)

Combine ship AIS dynamic data. The vessel voyage data used in this study were provided by the Changjiang River Administration of Navigational Affairs, which is under the Ministry of transport in China. These static data include the ship name, ship type, MD of departure, departure time, MD of destination, arrival time, and number of crew members. However, ship AIS data are not considered in this work. In future research, static data should be combined with AIS dynamic data to make the results more reliable.

(iii)

Enrich research data. The current research data only include the middle and upper reaches of the Yangtze River. In the future, data on the entire Yangtze River trunk line and even the entire inland water network can be obtained, and the research will be further deepened.

4.2. Application of the Finding of the Research

Ships operating in inland waters have an easier time obtaining support from the shore base than coastal ships do. Therefore, ships and shore bases should be taken into account while implementing collaborative preventative and control measures for ship domestic sewage. The proposed method has the potential to be applied for various purposes. The following countermeasures are suggested in light of the features of residential sewage from inland ships that were discovered throughout this study.

(i)

It is advised that the strategy of “storage on board and reception on shore” be adopted when designing and building new ships regarding ship sewage. It is recommended that ships that are currently in service undergo reformation to reduce pollution and eventually achieve zero discharge from the source. This will promote the building and application of green ships. Meanwhile, awareness of anti-pollution and the ability to operate anti-pollution equipment needs to be raised among crew members.

(ii)

According to the characteristics of ship arrivals and the characteristics of sewage discharges in different ports, the sewage-receiving capacity of ports should be reasonably optimized. For ports with a large sewage-receiving requirement, such as Chaotianmen, Baqu, Tongling, etc., the investment in sewage treatment should be increased, sewage disposal facilities should be further improved, sewage treatment stations should be expanded, and more professional sewage suction trucks should be purchased. Berthing ships should be provided with quick adapters for a free domestic sewage discharge pipeline to facilitate the ship’s quick connection to the suction truck and reduce the sewage discharge time.

(iii)

The establishment of a unified information platform for the supervision of sewage from ships will enable managers to understand the current operation of sewage treatment equipment and whether the data indicators of the equipment are normal according to the data displayed on the information platform, and on-site supervision by the maritime authorities will also be able to establish the focus of supervision based on these data. This means of information disclosure can largely improve the phenomenon of random sewage discharge from ships.

(iv)

The use of “Internet+” and technological means to improve the level of data management and control of domestic sewage discharge from ships, such as increasing long-distance video control, buoy positioning control, UAV control, automatic warning system of pollutants from ships, etc., to enhance the traceability, controllability, and openness of each process of disposal of sewage from ships and prevent the disposal task of domestic sewage from ships from becoming a mere formality. The full combination of ship domestic sewage management and modernized science and technology can improve the efficiency, convenience, practicality, and accuracy of the domestic sewage discharge work, and it is of great use to carry out all-round supervision of ship pollutants.

5. Conclusions

In this study, the ship sewage discharge characteristic complex network (SDCN) is firstly established based on ship voyage data provided by the Changjiang River Administration of Navigational Affairs. Secondly, the sewage discharge and reception characteristics in the Yangtze River have been analyzed. The topological analysis of the SDCN in the Yangtze River shows that it is a small-world network with the characteristics of a power-law degree distribution and a superliner betweenness-degree correlation. The top five MDs with the highest ship sewage reception are Chaotianmen MD, Tongling MD, Maanshan MD, Baqu MD, and Shashi MD. The sewage discharge between Chaotianmen and Baqu is the largest. The outcomes can be used to focus on the development of control mechanisms for the countermeasures of “zero discharge” for inland ships. They can also aid in our understanding of discharge characteristics of ship domestic sewage. Moreover, it can also shed light on some important planning and operational issues, such as optimizing the location of receiving stations or equipment to promote the wastewater treatment ability and decrease the subsequent biochemical treatment load.