Theory

Overview

The edges framework introduces a novel modeling layer in LCIA: exchange-resolved LCIA. Unlike traditional LCIA that assigns impacts to flows regardless of context, edges characterizes exchanges — the relationships between activities — allowing for CFs to reflect supplier/consumer location, activity classification, and scenario conditions.

This method is practical, scalable, and avoids the need for full GIS integration.

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Node-based vs Edge-based LCIA

Conventional LCIA applies CFs to nodes (flows), yielding:

\[s = \mathbf{c}^T \cdot \mathbf{B} \cdot \mathbf{A}^{-1} \cdot \mathbf{f}\]

Where:

  • \(\mathbf{f}\) is the demand vector

  • \(\mathbf{A}\) is the technosphere matrix

  • \(\mathbf{B}\) is the biosphere matrix

  • \(\mathbf{c}\) is a vector of characterization factors

  • \(s\) is the final score

This approach treats CFs as static, context-independent.

In contrast, edges defines a non-diagonal, rectangular matrix \(\mathbf{C}\) mapping to individual exchanges, enabling:

\[\mathbf{S} = \mathbf{C} \circ \mathbf{X}\]

Where \(\mathbf{X}\) is the matrix of exchanges, and \(\mathbf{S}\) is the characterized inventory.

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Matching Logic

Characterization factors in edges are matched using:

  • Supplier attributes: name, reference product, location, matrix

  • Consumer attributes: location, matrix, classifications

  • Contextual parameters: e.g., scenario-dependent variables like CO₂ concentrations

Matching is flexible: partial string matches (contains, startswith), matrix filters, nested dictionaries for classifications.

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Regionalization Mechanisms

Regional mapping follows a five-step cascade:

  1. Direct Match: Exact match on supplier/consumer location

  2. Disaggregation: Split aggregate inventory region using weighted CFs

  3. Aggregation: Fill missing CFs using containing regions

  4. Dynamic Resolution: Handle “RoW”-like fallback with exclusion logic

  5. Global Fallback: Default CF if no other match found

Weights can be based on population, GDP, water demand, etc.

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Symbolic and Scenario-Based CFs

CFs can be defined as symbolic expressions:

{
    "value": "GWP('CH4', H, C_CH4)"
}

Where variables (H, C_CH4) are evaluated per scenario or year.

This enables prospective LCIA consistent with IAM or RCP scenarios.

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Uncertainty Modeling

edges supports multiple uncertainty types:

  • normal, lognormal, triangular, uniform

  • discrete_empirical (e.g. basin-based CFs)

  • Nested uncertainty: e.g., a distribution selected per region, with per-basin variability

Monte Carlo draws are supported directly via CF definitions and sampling logic.

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Technosphere CFs

Beyond biosphere flows, edges can characterize technosphere exchanges — for instance, country-to-country commodity flows (e.g., GeoPolRisk). This adds relational, supply-chain-sensitive impact modeling.

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Life Cycle Costing (LCC)

In addition to environmental impact assessment, the edges framework supports life cycle costing (LCC) through the CostLCIA class. This allows the user to apply cost-based characterization factors to LCI exchanges, using the same regionalization and parametrization logic available for environmental LCIA.

Cost data can be:

  • Fixed (e.g., per unit cost in a specific currency)

  • Parameterized (e.g., price = base_price * inflation_factor)

  • Scenario-dependent (e.g., modeled price paths from IAMs or forecasts)

  • Uncertain (e.g., cost ranges or distributions used in Monte Carlo)

The core LCC workflow mirrors LCIA:

  1. Compute the inventory with lci()

  2. Match exchanges with cost factors via map_exchanges() (and mapping steps)

  3. Evaluate symbolic costs via evaluate_cfs()

  4. Compute the total life cycle cost using lcia()

  5. Export detailed cost breakdowns via generate_cf_table()

This allows integrated techno-economic and environmental modeling under consistent spatial, structural, and scenario assumptions.

Example:

import bw2data
from edges import CostLCIA

bw2data.projects.set_current("some project")
act = bw2data.Database("some db").random()

lcia = CostLCIA(
    method=("LCC 1.0", "2023"),
    demand={act: 1}
)

lcia.lci()
lcia.map_exchanges()
lcia.evaluate_cfs()
lcia.lcia()
df = lcia.generate_cf_table()
print(df.head())

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Summary

By resolving CFs at the level of exchanges, edges:

  • Enables context-aware LCIA without full GIS dependency

  • Supports regionalized, relational, and prospective modeling

  • Keeps logic transparent, reproducible, and extendable via JSON and symbolic expressions

This makes edges ideal for advanced LCIA applications where geography, classification, and policy scenarios all matter.