Benefit Index#

The Benefit Index expresses the value generated by ocean uses and realized on land. Although activities occur offshore, their benefits typically emerge at coastal hubs — cities, ports, processing centers, or other facilities where economic or social gains materialize. The framework focuses on this point of emergence rather than the full production chain, even when value may later accrue far from the coast.

English

_images/benefit.jpg — Conceptual elements of the Benefit Index. (a) Benefit suite: a hub receives a total benefit composed of multiple contributions from different users. (b) Single-source allocation: a user contributes benefit to one or more hubs from a single ocean area. (c) Multi-source allocation: a user with multiple spatial source areas distributes benefits to different hubs, creating a more complex benefit-flow structure.#

Português

_images/benefit_pt.jpg — Elementos conceituais do Índice de Benefício. (a) Portfólio de benefícios: um hub recebe um benefício total composto por múltiplas contribuições de diferentes usuários. (b) Alocação de fonte única: um usuário contribui com benefício para um ou mais hubs a partir de uma única área oceânica. (c) Alocação de múltiplas fontes: um usuário com diversas áreas espaciais de origem distribui benefícios para diferentes hubs, formando uma estrutura de fluxo de benefícios mais complexa.#

Users and Hubs#

In the PEM framework, a user is defined as an economic sector that operates in the ocean and possesses a characteristic set of practices and modes of use. A user is not an individual company. For example, fisheries as a sector constitute one user, even though many firms participate in it. Likewise, offshore wind energy, tourism, or maritime transport may each represent a distinct user.

Each user aggregates all activities of the sector but may operate across multiple spatial locations. These locations—specific patches or areas in the ocean—are referred to as sources of benefit. A single user may therefore have one or many sources, each contributing differently to the total benefit flow.

Ocean users are linked to Hubs through teleconnections: multiple activities can direct their benefits to a single location. A port, for example, may receive value from fisheries, offshore energy, tourism, and shipping. This set of benefits is referred as the the Hub Benefit Suite.

Benefit Allocation#

Two mechanisms describe how benefits flow from ocean space to hubs:

Single-source allocation. A user has one spatial source (e.g., a single fishing ground) but may distribute its benefits across multiple hubs. Part of the benefit may flow to one port, while the remainder supports another.

Multi-source allocation. A user consists of several spatial sources—such as multiple fishing areas or multiple offshore wind farms—each contributing differently to one or more hubs. This allows benefits to be partitioned according to the spatial origin of the activity.

Benefit Spatial Expression#

The spatial expression of benefits describes how the value generated by an ocean user is represented in geographic space once it is allocated to a hub. This expression depends on both the allocation mode (single-source or multi-source) and the spatial nature of the activity, ranging from well-defined operational areas to diffuse and continuous patterns.

Three main types of spatial expression are distinguished in the framework.

Polygon-based expression In multi-source allocation, benefits originate from multiple, spatially discrete source areas. These sources are typically represented as polygons, corresponding to well-defined and bounded operational zones. Examples include offshore oil and gas fields, wind farms, aquaculture sites, or licensed extraction areas. Each polygon represents an independent source of benefit, allowing contributions to be partitioned according to their spatial origin and combined consistently within the benefit-flow structure.

Kernel-density expression Some single-source activities generate benefits from localized points or linear features but influence surrounding ocean space in a gradual and distance-dependent manner. In these cases, benefits are represented using a kernel density approach.

Kernel density describes a process in which benefit intensity is highest near the source (e.g., coastal cities, ports, or tourism gateways) and decreases smoothly with distance, forming a continuous surface like a heatmap. This approach is suitable for activities such as coastal tourism, where benefits are emitted from specific coastal hubs but spread offshore without sharp boundaries.

Intensity surface expression Other single-source activities are not meaningfully linked to an emitting location but instead emerge from the cumulative intensity of use across the ocean space itself. These benefits are expressed as continuous intensity surfaces, often interpreted as fuzzy representations. Examples include industrial fishing effort, shipping density, or recurrent vessel traffic, where benefit generation reflects the spatial distribution of activity rather than proximity to a fixed source. Unlike kernel density, intensity surfaces are derived directly from observed or modeled use patterns within the ocean domain.

Together, these spatial expressions ensure that benefits can be represented in ways that reflect the operational reality of each sector, while remaining compatible with hub-based allocation and cumulative spatial analysis.

Benefit Assessment#

The Benefit Index is derived from an economic proxy \(E\) that quantifies the value that flows from the Users to the hub — such as jobs, tax revenue, or production measures — depending on available data. Information constrains may also require to define hubs at the level of coastal municipalities.

For a given hub \(i\), the Benefit Index is computed as the sum of the economic proxy \(E\) for all \(N\) Users \(j\).

\[B_i = \sum_{j = 1}^{N} \mathcal{B}(E_{i, j})\]

Where the function \(\mathcal{B}()\) converts the economic proxy into a unitless index.

Mapping the Benefit#

The Benefit Index must be mapped back to the ocean space, which requires identifying the spatial sources that generate the benefit flowing to each hub. In simple cases, a hub receives value from a single user and a single source; in real scenarios, multiple users and multiple sources commonly feed the same hub. Because these relationships are not always directly measurable, the framework relies on expert judgment to ensure that spatial allocations reflect actual sector practices and economic connections.

Once sources are defined, the Benefit Index concentrated at the hub can be translated into Benefit Density in the ocean space model, which expresses how much benefit is generated per unit area. Large source areas with modest benefit yield low density, while small yet productive areas produce high density. Thus, two sources may contribute the same benefit to a hub but differ sharply in density due to their spatial footprints. Benefit Density highlights how efficiently ocean space is used and helps identify activities that deliver high value with lower spatial pressure.

Each hub produces its own Benefit Density map, showing where and how intensely ocean areas contribute value to that hub. Using map algebra (e.g., summing layers), the individual hub maps can be added to generate the Accumulated Benefit Density surface, capturing the overall economic productivity of the ocean space across all hubs and users.