Sea-land interdependence and delimitation of port hinterland-foreland structures in the international transportation system

2.1. The spatial structures of the port system

The port-hinterland relationship has been studied to address how the economic growth of surrounding urban regions occurs in relation to the functioning of a port system. The classical port development model of Bird (1980) and Taaffe et al. (1963) depicts a port system with differentiated spatial structure where locational advantage induces agglomeration of economic activities, urban expansion and economic growth of nearby port areas. The locational advantage of lower freight costs in the vicinity of ports is considered a driving force of the symbiotic relationship between ports and hinterlands, and of business co-location that bolsters urban agglomeration activities near ports (Hesse, 2010; Ng et al., 2014). In line with this notion, spatial structures of the port system have been captured by simply delineating a port's surrounding region as the port's exclusive service area based on physical proximity (e.g., Niérat, 1997).

As the modern international transportation system has advanced, researchers started to question the classical port development model that suggests a simple bilateral landside interaction between ports and hinterlands (see Robinson, 1970; Vigarié, 1979; Charlier, 1992). They argued that spatial dynamics of the port system should be understood in the wider spatial extent framed by shipping flows to and from the ports. In an early study, Robinson (1970) argued that hinterlands and forelands cannot be comprehended separately but are interdependent instead, since shipping flows between hinterlands and ports are part of the whole logistic process spanning across land and water. He observed that destinations of the import flows through Vancouver from Japan were spatially distributed very differently from those from the United Kingdom and those from all other countries. His analysis concluded that the hinterland distribution strongly depends on characteristics and directions of freight flows from forelands.

In the same spirit, Vigarié (1979) proposed the port triptych model to refer to an inseparable relationship between a port, its hinterland and its foreland. The model suggests that depicting the spatial structure of a port system by delimiting a hinterland based on the physical proximity from ports is flawed. Instead, the spatial structure of a port system should regard landside transportation flows to ports as a part of the entire transportation flows across land and water. Charlier (1992) also pointed out that segmenting traffic flows to and from ports may disregard the modern logistic chain, intermodal transport and feedering practices. In sum, ports are no longer viewed as central places connected in simple ways to their hinterlands.

The notion of the port triptych has been further extended in the context of the modern port system as Notteboom and Rodrigue's (2005) conceptual model of port regionalization. Acknowledging the rising importance of inland distribution centers, they argued that port development takes place in a way that port terminals establish integrated network connections with inland ports and distribution services distributed in extensive inland areas. The proposed port regionalization model posits that the spatial extent of the port system goes beyond the vicinity of the ports and can be extended to a wider regional scale. Challenging the hinterland-foreland dichotomy, Rodrigue and Notteboom (2010) extended the port regionalization model to address logistic integration not only on the landside with inland distribution centers but also on the seaside with intermediate hub ports. As hinterlands are structured by regionalization of port terminals and inland distribution centers, they argued that a cluster of ports are also regionalized as a result of the inter-port logistic integration between feeders and hubs on forelands. Considering that containerization and intermodal transportation are strongly linked to the functions of inland distribution centers and hub-and-spoke distribution systems, hinterland-based and foreland-based regionalization are not separate but coupled and interdependent phenomena in effect, as argued by the port triptych thesis (Rodrigue and Notteboom, 2010). Monios and Wilmsmeier (2012) argued that port regionalization may take difference forms according to the development strategies of governments, port authorities and maritime and land shipping lines, and according to the institutional relationships between them. Raimbault et al. (2016) highlighted the importance of institutional relations of shippers and logistics providers across land and water in creating integrated logistics chain and shaping port regionalization.

There are well grounded theories pointing to port triptych structures as emerging from the contemporary state of the logistic process across sea and land, but empirical validation is still quite limited. For example, Ducruet and Zaidi (2012) suggested that the emergence of port systems and foreland-side spatial structures can be apprehended by the network structure of inter-port flows, but their analysis was focused on capturing the clusters of the maritime network and did not address landside flows and ensuing hinterland-side structures. Guerrero (2014) proposed 4 types of French hinterlands mainly based on the magnitude of how landside transportation flows from hinterlands to ports are diminished by distance, without considering how the shipments forwarded from land are transported on the maritime side. Ducruet et al. (2015) proposed a typology of port regions based on local socioeconomic characteristics and ports' commodity specialization with no regard for patterns of land and maritime transportation flows to and from ports. Santos and Soares (2019) presented a methodology for delimiting hinterlands by calculating the minimum generalized costs from load centers to different container terminals, but comprehensive patterns of both maritime and land shipping flows are not considered in their analysis. Berli et al., 2018, Berli et al., 2020 analyzed the centrality and accessibility of ports and cities that arise in the sea-land intermodal network by taking both landward and seaward shipping flows into account. Thus, even though the port triptych is a well acknowledged concept in international transportation studies, empirical studies have rarely addressed the whole shipping process across land and water.

2.2. Network-based regionalization: methodological and modeling perspective

The functional regionalization research aims to understand how regions are organized around nodal locales based on socioeconomic and functional relationships between areas (Fox and Kumar, 1965; Brown and Holmes, 1971; Cliff et al., 1975; Haggett et al., 1977; Masser and Scheurwater, 1980; Hoover and Giarratani, 1984; Cliff and Haggett, 1998). Spatial structures are captured by discretizing the continuous space into a group of discrete regions and by presenting underlying structures of spatial patterns and socioeconomic relationships, especially highlighting spatial heterogeneity, functional divisions, hierarchies and spatial interactions among the identified regions (Farmer and Fotheringham, 2011).

Recent functional regionalization studies have explicitly incorporated the network science approach to better trace spatial structures based on the multi-adic network structures between areas. For example, Farmer and Fotheringham (2011) introduced the network science concepts of modularity and community structures (Newman, 2004, Newman, 2006) to identify functional regions by qualitatively distinguishing intra- or inter-regional commute patterns. De Montis et al. (2013) applied a community detection algorithm to a commute flow network to reveal functional regions that emerge from the human mobility patterns. Community detection algorithms were also adopted to detect functional regional differentiation based on the spatial interaction of mobile phone data (e.g., Gao et al., 2013; Sobolevsky et al., 2013; Chi et al., 2014). Likewise, based on the observation of spatial interactions of social media activities, Shen and Karimi (2016) developed a regionalization method based on multidimensional network measures, and Liu et al. (2014) presented a regionalization pattern of the human mobility in China by employing a community detection algorithm. Bergmann and O'Sullivan (2018) used the stochastic blockmodel to detect functional regions formed by the network structures of both migration outflow and inflow patterns between counties. Adopting the network science approach enables to consider network structural features made by flow relationships among more than two entities in the functional regionalization, such as network clustering, centrality, hierarchies, intermediacy, structural equivalence, structural holes, in contrast to more traditional approaches that simply detect bilateral flows between origin and destination areas.

Even though international transportation has rarely been studied from the functional regionalization perspective, there is increasing research that applies the concepts of network science and geographic information science. Ducruet et al. (2010b) pointed out that new concepts and methods of network science from physics had not been fully adopted in maritime geography despite the network nature of global maritime shipping. The graph visualization and network-based centrality measures were suggested to address hub-and-spoke structures and port hierarchy in the Atlantic (Ducruet et al., 2010b) and Northeast Asian (Ducruet et al., 2010a) maritime transportation systems. Ducruet and Zaidi (2012) applied the topological decomposition method to the international maritime shipping network and reinterpreted results as the foreland-based regionalization of ports in the context of complex network science. Ducruet and Notteboom (2012) also presented clustering maps and spatial distribution of degree centrality measures of ports at the global scale that show how port systems integrate foreland localities and form foreland-based spatial structures through the global maritime transportation network. The long-term evolution of the maritime transportation systems from 1890 to 2010 is also examined through the single linkage analysis (Ducruet et al., 2018). Community detection algorithms were also adopted to explore the hinterland-side regionalization based on the trajectory records of U.S.-bounded export cargo shipping (Jung et al., 2018). Techniques of network-based geographic information science have been applied to reveal sea-land network characteristics of port systems and intermodal shipping flows by integrating spatial data of road and maritime route networks and spatial data of freight shipping flows across land and water (Shen, 2013; Berli et al., 2018, Berli et al., 2020; Shen et al., 2020).

To overcome the design limitations of earlier studies, we use the stochastic blockmodeling (SBM) approach to functional regionalization. The SBM shrinks a complex network into a simplified block-to-block network where sets of nodes are reduced to blocks according to similarity in directions and cohesion of network flows. It has been widely used in various studies examining the relational structures in various contexts such as human migrations (Bergmann and O'Sullivan, 2018), the global city network (Zhang and Thill, 2019) and the brain network (Faskowitz et al., 2018). In the context of international transportation, the SBM approach can detect the embedded network structure among groups of origin localities depending on the same port systems, corresponding forwarding ports and intermediate ports. Due to its flexibility in detecting various types of network structures, it can account for the complex functional connections among landside and seaside networks, simultaneously.

3.1. Data

We take the case of maritime shipping from Europe to the U.S. to study the concept of port triptych. The Port Import Export Reporting Service (PIERS) Trade Intelligence database contains individual records of door-to-door containerized shipping from product sources in Europe to the U.S. ports. Due to their detail in shipping trajectories, PIERS data have been used to investigate port choice patterns of inland cargo shipping in Europe (Kashiha and Thill, 2016; Kashiha et al., 2016a; Kashiha et al., 2016b) and in the evaluation of quality of inland transport systems in South America (Tiller and Thill, 2015). Through this database, the path of each bill of lading can be tracked down to 4 nodal locations: source of shipping (O), first forwarding port (P1), intermediate port (P2) and U.S. destination port (PUS). These disaggregated trajectories allow us to trace the spatial interaction relationship between forwarding ports, on the one hand, and corresponding source localities in port service areas and transshipment points on the way to the U.S. port of entry, on the other hand.

The dataset includes a variety of shipments that takes different shipping routes and transshipment patterns, but we exclude outlier shipment cases that occur rarely. The outlier cases tend to occur mostly once but have quite peculiar shipping behaviors. In effect, they are akin to noise over which the network model would struggle to maintain its statistical power. Also, since small ports only have very few shipments, it is difficult to precisely capture connectivity patterns in the network. Hence, we filtered out shipment cases that do not directly cross the Atlantic and are transshipped instead at ports in other regions than Europe, such as Asia, South Africa and South America. Because of the peculiarity of the shipping behavior, we also excluded shipment cases from small islands and only included shipment cases that originated from mainland Europe and from British Isles. Shipment cases were also removed if they were shipped through extremely small ports that were found to process only one or two shipments in our original dataset. We filtered out shipment cases if either forwarding or intermediate port is out of the 99.5th percentile by port throughput.

In this research, we use the containerized shipment cases from Europe to the U.S. in October 2006. From an original dataset comprising 106,602 bills of lading, the removal of outliers leaves 103,359 bills of lading, from 12,501 origin localities, 80 forwarding ports, 27 intermediate ports, to 35 U.S. ports of entry. The total shipment volume is 195,921.8 Twenty-foot Equivalent Units (TEUs).

3.2. Construction of sea-land shipping network data

We compile a shipping network on the containerized shipment data that describes the shipping paths across land and sea (O-P1-P2-PUS). The network data encompass nodes of landside shipping sources and ports links of the landside and maritime shipping flow. The links have three different components¹: 1) landside shipping flows between source nodes and first forwarding port nodes (OP1), 2) seaside flows between first forwarding port nodes and intermediate port nodes before cargo departs to U.S. ports (P1-P2) and 3) seaside long-haul trip to a U.S. port (P2-PUS). In case of direct shipping without transshipment, the first forwarding port and the intermediate port are coded identically (P1 = P2).

This leads us to construct two networks based on the respective flow components: the landside shipping network (O-P1) and the maritime shipping network (P1-P2 and P2-PUS). Total cargo shipping is aggregated by origin-destination dyads in these networks. In the hinterland shipping network, we do hexagonal binning of the shipping sources by 25 km radius to standardize their geographical units. Administrative units of each country can be quite varied as they reflect their own socio-political context. Since the geographical scope of this study is that of large economic spaces, using geographically standardized units is an appropriate strategy to avoid the biases associated with the modifiable areal unit problem. The locations of shipping sources are identified by the city names of their shipping addresses, which is prone to deviation from their real production or shipping origins. In addition to standardizing geographical units across the European space, the hexagonal binning approach also enables to reduce spatial uncertainty due to the positional errors of geocoding the shipping addresses.

By way of their interface at the ports, the landside and maritime shipping networks are then integrated as a single sea-land shipping network. While numerous source nodes send their shipping to far fewer forwarding ports, ports send or receive shipping according to whether the shipping is transshipped. By this network construction process, we gain a sea-land shipping network with 2262 nodes and 6483 links, including 2143 source nodes, 119 port nodes, 5569 landside links and 914 maritime links.

3.3. Method: nonparametric weighted stochastic blockmodel

The SBM is a statistical network model that estimates embedded network block structures by partitioning nodes based on network flow patterns, structural equivalences (topologically similar positions) and community structures marked by strong cohesion among nodes (Karrer and Newman, 2011). As a data generalization technique, it can be compared to principal components analysis, which reduces the number of variable dimensions into main principal components, and to cluster analysis, which classifies similar observations with similar scores to the same group. Similarly, the SBM assigns nodes and links in the original network to blocks and block-to-block links in the block network. Since we argue in support of the view that maritime shipping is a hinterland-foreland continuum and in support of the concept of port triptych in the port system (Robinson, 1970; Charlier, 1992), the SBM is well suited as it offers the advantage of handling all origin-destination links of the shipping trajectories on both hinterland and foreland sides. It assigns each node into a single block based on similarity in their connectivity patterns, each identified block indicates a group of source or port nodes sharing similar landward or seaward shipping patterns in the sea-land shipping network. Thus, the original network with many nodes and links is simplified and reduced to a shrunk network of a reduced number of blocks and between-block links, and the whole network structure is understood with the block-to-block shrunk network. Examining connectivity between the identified blocks helps us to understand components of the port triptych structures.

We adopt the npWSBM proposed by Peixoto (2018), which finds the embedded network block structures based on the quantified strength of the edge weights without prior setting of the number of network blocks. The npWSBM can detect network structures based on not only community structures but also structural equivalences, through which it is possible to find the hierarchy and functional differentiation of ports and the clustering of hinterlands and ports. The network block structure is estimated nonparametrically by finding the optimal partition from the observed hierarchical structure of the given weighted network, unlike the weighted stochastic block model of Aicher et al. (2015) that requires the prior setting of the number of blocks (Peixoto, 2018). Since shipping from a certain locality may be contested between different ports (Wan et al., 2018), we use the containerized cargo volume (TEUs) as the network weight.

Let us consider a global cargo shipping system. It can be represented by a directed graph G = G(N, A, Ω, b) where N is a set of nodes of sources and all ports, A is a binary adjacency matrix whose element a_ij = 0 or 1 indicates the dyadic connectivity between i and j; Ω is an edge weight matrix whose element ω_ij ∈ ℝ indicates the continuous real weight of a_ij, and b is a vector of embedded block memberships of all nodes which are to be determined. The graph G is assumed to be generated conditionally upon the latent block structure:(1)$P\left.\mathit{A},\mathit{\Omega }|\mathit{b},\mathit{\theta },\mathit{\gamma }\right)=P\left.\mathit{\Omega }|\mathit{b},\mathit{\gamma }\right)P\left.\mathit{A}|\mathit{b},\mathit{\theta }\right)$and(2)$P\left.\mathit{\Omega }|\mathit{b},\mathit{\gamma }\right)={\prod }_{\mathit{rs}}P\left.{\mathit{\Omega }}_{\mathit{rs}}|{\mathit{\gamma }}_{\mathit{rs}}\right)$where θ and γ are two sets of parameters that characterize the probability distributions of a_ij and ω_ij for all i, j ∈ N, respectively, Ω_rs is an edge weight matrix among nodes in the blocks r and s, γ_rs is a set of parameters that characterize the probability distribution of the edge weights between r and s. It should be noted that the weight ω_ij is sampled conditionally on γ only when the corresponding edge exists. P(A| b, θ) indicates the generation of the unweighted graph based on binary graph connectivity only.

The npWSBM is premised on a hierarchical structure in the network blocks (Peixoto, 2014). The hierarchical structure detected by the npWSBM is illustrated in Peixoto (2014), (Fig. 1). In this view, each node i is nested into level-1 blocks, each of which is again nested into level-2 groups until it reaches level L, which has a single block. Thus, all levels of nodes/blocks are mutually exclusive sets that are exhaustively nested into their higher blocks. The lower block is estimated from the estimated upper block, so it does not require a priori setting of the number of blocks. The embedded block structure parameter b can be specified by the following L-level block structure (Peixoto, 2018):(3)$\mathit{b}\equiv \left.{\mathit{b}}^l\right\}=\left.{\left.b_i^{\left.l\right)}\right\}}_l|i\in N,l\in \left.1,\cdots ,N\right\}\right\}$where b_i^(l) is a block membership of node i at level l such that b_i^(l) ∈ {1, ⋯, B_l} and B_L = 1. A L-level set of parameters characterizes the edge weight distributions in each block of each level, γ = {γ^l} with ${\mathit{\gamma }}^{L+1}\mathit{=}\left.\widehat{\mathit{\gamma }}\right\}$ being a single hyperparameter at the topmost level. Each γ^l is generated by the following probability, conditional to the setting of its higher-level block-to-block graph:(4)$P\left.{\mathit{\gamma }}^l|\mathit{A},{\mathit{b}}^{l+1},{\mathit{\gamma }}^{l+1}\right)={\prod }_{\mathit{rs}}P\left.{\mathit{\gamma }}_{\mathit{rs}}^l|\mathit{A},{\mathit{b}}^{l+1},{\mathit{\gamma }}_{b_r^{\left.l+1\right)}{b}_s^{\left.l+1\right)}}^{l+1}\right)$where b_r^(l+1) and b_s^(l+1) denote the (l + 1)-level blocks to which the l-level blocks r and s belong. Using a nonparametric Bayesian inference approach and a priori hierarchical structure, b^∗ ≡ {b^l}^∗ can be obtained through maximizing the following Bayesian posterior probability (Peixoto, 2018):(5)${\left.{\mathit{b}}^l\right\}}^{\ast }=\underset{\left.{\mathit{b}}^l\right\}}{\text{argmax}}P\left.\left.{\mathit{b}}^l\right\}|\mathit{A},\mathit{\Omega }\right)=\underset{\left.{\mathit{b}}^l\right\}}{\text{argmax}}\frac{P\left.\mathit{A},\mathit{\Omega }|\left.{\mathit{b}}^l\right\}\right)P\left.\left.{\mathit{b}}^l\right\}\right)}{P\left.\mathit{A},\mathit{\Omega }\right)}.$

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Fig. 1. Schematic hinterland, port and U.S. port blocks in the sea-land shipping network.

Since P(A, Ω) is not computationally feasible, the optimal solution {b^l}^∗ can be obtained through the Metropolis-Hastings algorithm, which compares the likelihood ratio between two stochastically generated solutions. For detail on the algorithm for the optimal solution, see Peixoto (2018).

3.4. Estimation issues and determination of best-fit results

Since the Metropolis-Hastings algorithm uses a random assignment, the npWSBM may generate inconsistent block memberships in each iteration. In order to obtain consistency of the estimation results, we take the block result from the posterior distribution generated from multiple iterations of block results. After running a model 10,000 times to generate the posterior distributions, we obtain a block result by averaging the 10,000 block membership results.

To find the best-fit model that represents the network block structure, we consider six edge weight distributions for the edge weight matrix Ω: normal, log-normal, exponential, Poisson, binomial and geometric distributions. For each weight distribution, we obtain a block result from the 10,000 iterations and measure the goodness-of-fit by the log likelihood scores. Of the six sets of results, we choose the one that gives the highest log-likelihood scores as the best-fit edge weight distribution.

Even though the npWSBM can innately and non-parametrically find the optimal number of blocks, we should consider if the result of the optimal block number is externally valid with regard to spatial distributions of ports and sources. Since the npWSBM only considers network connections between nodes and their structural equivalence, not their spatial locations, it is possible that the results are difficult to interpret if geographically distant nodes (ports or sources) are assigned to the same block. To mitigate this issue, we find the most interpretable network block membership by adjusting the number of blocks around the optimal number and then by visually checking the spatial distributions of block memberships. The model estimation was implemented with the Python library graph-tool module (Peixoto, 2022).

4.1. Contextualization of the network blocks and calibration of the stochastic blockmodel results

Of the six edge weight distributions assessed, the log-normal model is found to have the highest log-likelihood values, indicating the best model fit among all edge weight distributions (Table A1). Hence, we choose this distribution for the rest of the analysis. While the global optimal result includes 18 blocks, we check whether this solution is sufficiently interpretable and presents good external validity. In addition, we generate a series of solutions by externally imposing the number of blocks in the range of 10 to 65, and calculate the associated log-likelihood values. The log-likelihood is highest with 18 blocks (123 links), the global optimum (Fig. A1). The second and third best solutions are obtained with 20 and 24 blocks (136 and 155 links), respectively.

The three sets of npWSBM results present that source nodes, non-U.S. port nodes and U.S. port nodes are completely partitioned into different blocks; all nodes assigned to each block are the same type. This shows that the npWSBM discerns the difference in connectivity patterns of the three types of nodes: 1) a group of source nodes send shipments to port nodes (dubbed ‘hinterland block’ hereafter); 2) a group of non-U.S. port nodes receive landside inbound shipments from source nodes and seaside inbound shipments from other port nodes simultaneously, and also send seaside outbound shipments to other port nodes (‘port block’ hereafter); and 3) U.S. ports only receive maritime shipments from non-U.S. ports (‘U.S. port block’ hereafter). Given that the whole sea-land shipping network can be split into modules of hinterland, port blocks and U.S. port block, the port triptych structure can be understood as a collection of hinterland, port blocks and U.S. port block and connections between them. Based on the npWSBM results, we can further categorize three types of port blocks: feeder, hub and gateway blocks (Detailed characteristics of three types of port blocks are described later). The schematic illustration of hinterland, port and U.S. port blocks consistent with this conceptualization is presented in Fig. 1.

The global optimal log-normal model identifies 18 blocks embedded in the Europe-U.S. freight shipping network, 6 hinterland blocks, 11 port blocks and 1 U.S. port block. The spatial representation of the npWSBM results depicts hinterland and port blocks with their geographical extent and shipping characteristics (Fig. A2). Despite having the highest log-likelihoods, we find that the solutions with 18 and 20 blocks are limited in representing the full reality of the European port system, especially in its eastern part (Fig. A2). Even though these results are the two best from a statistical criterion perspective, they have poor ability to depict that Balkan and Baltic ports are physically separate and that they actually constitute different port systems in the East Mediterranean and Baltic seas. It can be argued that Balkan and Baltic ports have in common to serve contiguous but peripheral territories surrounding the economic core of Europe as feeders to other hub ports.

This leads us to turn to the third optimal solution, which encompasses 24 blocks, as the solution worthy of consideration for the rest of our analysis. This solution identifies 9 hinterland blocks (blocks A–I), 14 port blocks (block 1–14) and 1 U.S. port block (block 15) (Fig. 2). Balkan and Baltic ports are assigned to distinct port blocks 2 and 3, respectively, and the eastern landside areas are split into Balkan (block A) and Baltic areas (block B). This provides more interpretable results where we can capture the spatial structure between hinterland, forelands and ports more meaningfully.

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Fig. 2. Spatial representation of the hinterland and port blocks from the final stochastic block modeling results (25 blocks) (Note: Land areas with no color indicate that no shipment is sourced from those areas. Shipments from small islands are excluded from the analysis).

As a final step, we check if the detected port blocks have sufficient cohesion without any outlier nodes. We measure the cosine similarity in the block-to-block connection between each port node and their assigned block to see if individual port nodes have significantly different connectivity patterns from those of the block they are assigned to. The cosine similarity is 0 when a port node has a connectivity pattern uncorrelated with that of their assigned block; it is 1 when a port node has a perfectly correlated connectivity pattern. All port nodes, except Bordeaux and Newcastle, have a cosine similarity above 0.5, indicating a high level of cohesiveness to the assigned block. Bordeaux and Newcastle have low cosine similarity scores (0.146 and 0.367, respectively) that indicates that they have a significantly different and peculiar connectivity pattern from the rest of their block. This is probably because these ports serve their localized hinterlands destined to the U.S. by shipping Bordeaux wine and Newcastle brown ale, respectively. Hence, Bordeaux and Newcastle are excluded from their block membership and are left as unassigned isolate nodes (block 16).

4.2. Characteristics of hinterland and port blocks

As shown in Fig. 1, we categorize the port blocks by their role in the whole shipping network based on the preponderance of transshipment activities. The following conventions are used. When a block's ports receive and forward landside freights to other ports for transshipment more frequently than the average (19.94%), they can be considered feeder block. If a block's ports receive and transfer maritime freights to U.S. ports of entry more frequently than the average, we define the block as a hub block. When a block transfers both landside and maritime freight less frequently than the average, the ports forward shipments directly to U.S. ports of entry, and we call the block a gateway. Considering that the ports of Antwerp and Rotterdam (block 1) transfer substantial amounts of maritime shipments from other ports to U.S. ports (15.52% of the total transshipments), and that Hamburg and Bremerhaven (block 8) forward significant amounts of landside freights directly to U.S. ports of entry, blocks 1 and 8 are considered to have characteristics of both gateway and hub, so they are classified as a gateway-hub blocks. Because of the geographical remoteness from Europe, we categorize the ports in block 14 as offshore hubs.

4.3. The network block structure of the port system

We now examine how hinterland and port blocks are integrated in the sea-land shipping network and constitute the whole port system in Europe. To this end, nodes and links are aggregated by blocks, and the node-level network is reduced to the block-level shrunk network (Fig. 3). The visualization of the block-level shrunk network leads a number of findings about the spatial structure of the port system in Europe.

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Fig. 3. The block-level shrunk network of the sea-land freight shipping system of Europe. Squares, circles, triangles, and diamonds stands for blocks of diverse types. They are labeled according to the lists in Table 1, Table 2. (Note: The network is visualized with Fruchterman-Reingold layout).

First, we find that trade shipments are structured via the dominant role of a few large port blocks. In our dataset of U.S.-bound shipments, the U.S. ports receive 69.9% of the total shipment volume from port blocks 1, 8 and 11 as the last port of export, including Antwerp, Rotterdam (block 1); Hamburg, Bremerhaven (block 8); Genoa, La Spezia and Leghorn (block 11). This is not just because these blocks process landward shipments from their own hinterlands, like blocks D, E and F, but also process cargo transshipped through other feeder blocks. Especially, blocks 8 and 11 are found to be the main intermediate nodes between U.S. ports, feeders and hinterlands, indicating their critical role as hubs in the European port system.

Second, Europe's trade logistics is driven by the hub-and-spoke system where a few hub ports and many feeder ports hold complementary functional division. The node-level shrunk network (Fig. 3) shows a functional division in the trade logistics between a few hubs and many feeders represented by the block-to-block connection. We find hub or gateway blocks (1, 7, 8, 11, 12 and 14) near the center of this network (block 15), which stands for the whole set of U.S. ports of entry to which they have direct shipping lines. We also find feeder blocks (2, 3, 4, 6, 10 and 13) placed at the periphery around the corresponding hub blocks, whose feeder operations are tied to. The hub blocks do not only serve hinterland blocks but they also mediate shipments between U.S. ports and feeder blocks as maritime transshipment points. In contrast, the feeder blocks are positioned between hinterland blocks and hub blocks, indicating a role in providing feeder operations that forward shipments to hub ports. The connection among feeder and hub blocks shows how feeder and hub ports maintain a complementary multi-adic relationship via the logistic integration for the whole shipping process.

Third, while some hinterland areas have direct access to the shipping lines to U.S. ports, others have indirect access through the feeder ports. Hinterland blocks D, E and F maintain a strong tie to hub or gateway blocks directly connected to the U.S. ports (11, 1, 5 and 8); on the other hand, hinterland blocks at the periphery (A, B, G and I) of the shrunk network are mainly connected to feeder blocks, not hub nor gateway blocks. The former hinterlands are the areas where direct shipping line services to the U.S. are provided, but the latter hinterland blocks have limited direct access to the shipping lines to the U.S.; thus, most of their shipments can reach U.S. ports through transshipment via feeder and hub blocks. Hinterland blocks A, B, G and I are direct hinterlands of the feeder blocks 2, 4, 6 and 10, respectively, but at the same time, they also can be considered as indirect hinterlands of hub blocks 12, 8, 7 and 1, respectively, because their shipments to the U.S. should be transshipped through these hub blocks.

4.4. Block-to-block trajectory and hinterland-foreland continuum

Adopting the concepts of hinterland-foreland continuum (Robinson, 1970) and port triptych (Vigarié, 1979), we examine the entire trajectory of all shipments across land and water to comprehend the foreland-hinterland continuum structure of the European port system. On the aggregate, we track the block-level shipment flows departing from each hinterland and their flow patterns throughout the shipping trajectory from sources to U.S. ports of entry. By matching each of the 4 nodal locations (O-P1-P2-PUS) in the shipments' sequence to their assigned block, we produce an alluvial plot that tracks block-to-block shipment flows (Fig. 4). The group of flows departing from each hinterland block is color-coded to trace patterns through en route nodal points to the final U.S. ports of entry. Direct and transshipped shipments are separated to better illustrate flow patterns. Based on the block-to-block shipping trajectory patterns, the hinterland-foreland continuum structures in the European economic space are described as follows.

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Fig. 4. Alluvial plot of block-to-block shipment flows: (a) Direct Shipment Flow, (b) Transshipment Flow.

Block A (Balkan area) is the area mainly served by the hub-and-spoke distribution system of Naples-Gioia Tauro, where port blocks 2 and 12 work together in the East Mediterranean area. Since the ports on the Balkan coast lack long-haul shipping lines to the U.S., the shipments exhibit patterns of being first forwarded to the feeder ports in block 2, and then transferred to the hub ports in block 12. Even though Naples and Gioia Tauro (block 12) are located in Italy and are topographically separated from the block A, they are transit points on the maritime routes to the U.S. and have a locational advantage in being hub ports for shipments sourced from block A.

Block B (Baltic-Scandinavia) depends on the hub-and-spoke distribution system of Bremerhaven-Hamburg (block 8) interfaced with port blocks 3 and 4 to serve the Baltic Sea area. Freight flows from block B account for the largest share of the total transshipments handled by the latter two blocks. While very few shipments are directly shipped to the U.S. through ports in blocks 4 and 8 (Fig. 4-(a)), most shipments are shipped by the feeder operations of blocks 3 and 4 and then transshipment at Bremerhaven or Hamburg (block 8). The ports in both blocks 3 and 4 are primarily dedicated to feeder operations exclusively for connecting block A and Bremerhaven-Hamburg. Given that a few shipments are directly shipped through ports in block 8, the latter plays a very limited role as a local hub by providing long-haul shipping lines to the U.S.

Block C (Italy) covers a hinterland area that generates a smaller amount of shipments than block D. This area does not depend on a single shipping channel to the U.S., so the hinterland-foreland structure is quite complex. A small volume of shipments are directly forwarded to the U.S. through Genoa-La Spezia-Leghorn (block 11) and Naples-Gioia Tauro (block 12). As for block A, this area also depends on a shipping process through the hub-and-spoke distribution systems of Genoa-La Spezia-Leghorn (block 11), supported by the feeder operations of blocks 12 and 13, and Naples-Gioia Tauro (block 12), supported by block 13.

Italy's Northern industrial areas (Block D) shows a direct hinterland area exclusively served by Genoa-La Spezia-Leghorn (gateway block 11). While a few shipments are processed through transshipment from block 11 to 14 and from 13 to 12, the dominant volume of shipments are directly shipped through block 11. The port functions of Genoa-La Spezia-Leghorn work as a main gateway for block D by exclusively providing a direct access to shipping lines to the U.S. without the need for transshipment.

The Netherlands and Western Germany (block E) constitute a direct hinterland area of two main gateway-hub blocks, namely Antwerp-Rotterdam (block 1) and Bremerhaven-Hamburg (block 8) (Fig. 4(a)). Placed between the two gateway-hub blocks, this area has a high level of direct access to the two port blocks' direct shipping lines to the U.S.; very little of its freight is transshipped. Benefitting from this great accessibility advantage, this area is found to generate the largest shipment volume to the U.S. of all hinterland blocks. Given that the shipping flows are bifurcated to two streams into the two gateway-hub blocks, this area is an overlapping hinterland where those gateway-hub ports fiercely compete with each other.

Block F (Belgium-France) marks a direct hinterland area served by Antwerp-Rotterdam (block 1) and Fos-Le Havre (block 5) that provide direct shipping lines to the U.S. A few shipments confined to the Western Mediterranean are observed to be transferred between blocks 5 and 7, where Fos serves as a feeder port towards the three large Spanish hubs, but the amount is not significantly large. This block is the area where four main gateway ports compete and attract shipments from different directions: Le Havre attracts shipments from the North, Fos from the South, and Antwerp-Rotterdam in the Northeast. Despite the small amount of transferring shipments, similarly to block E, this area can be considered an overlapping hinterland of Antwerp-Rotterdam (block 1) and Fos-Le Havre (block 5).

Shipments from block G (Iberia) depend on the complementary operation of port blocks 6 and 7, distributed along Spanish and Portuguese coastline. Similar to the block C, there are multiple shipping channels to the U.S., and the hinterland-foreland structure is complex here too. The shipments are both directly shipped and transferred through feeder-hub connections. While the direct shipments tend to sail through Algeciras-Valencia-Barcelona (block 7), large hub ports in the Western Mediterranean, shipments that are transshipped have a pattern of first being forwarded to feeder ports in block 6 and then transshipped at the hub ports in block 7. Limited cargo is transferred at other port blocks, namely 1, 5 and 14. Thus, block G is integrated with the hub-and-spoke system of Algeciras-Valencia-Barcelona where block 6 offers feeder operations and block 7 provides a hub function.

Similar to block G, the shipments from blocks H and I (Inland and Coastal British Isles) are both directly shipped and transferred through feeder-hub connections. Block H mainly serves as the direct hinterland area of block 9, while block I represents a hinterland area served overwhelmingly by the feeder operation of block 10 and the hub function of Antwerp-Rotterdam (block 1). While block 10 is dedicated to feeder operations in the British Isles (Fig. 4(b)), block 9 assumes the role of local hub by providing long-haul shipping services and processing shipments transferred from block 10. However, a dominant share of the transferring shipments is processed through non-local hub ports, Antwerp-Rotterdam (block 1), rather than domestic local hub ports in block 9. Thus, block H depends on block 9 for direct long-haul shipping service to the U.S., while block I is part of the hub-and-spoke distribution system of Antwerp-Rotterdam, where block 10 provides feeder service.