Exchange Sign Conventions

This document explains the exchange amount sign conventions used in EcoSemantic and demonstrates how they align with standard LCA practice and the underlying Brightway2 calculation engine.

The Simple Rule

Use Positive Values

In EcoSemantic, use positive values for:

• ✅ Material and energy inputs consumed by your process
• ✅ Emissions released to the environment
• ✅ Reference products (outputs) produced by your process

Negative Values are Special Cases

Use negative values only for:

• Avoided burdens (substitution/system expansion)
• Credits from recycling scenarios
• Co-product allocation adjustments

Quick Reference Table

Exchange Type	What it Represents	Amount Sign	Example
production	Reference product output	Positive	amount=1.0 (1 kg product)
technosphere	Material/energy input	Positive	amount=5.0 (5 kWh electricity)
technosphere	Avoided production	Negative	amount=-2.0 (avoided 2 kg steel)
biosphere	Emission to environment	Positive	amount=10.5 (10.5 kg CO₂)
biosphere	Resource from nature	Positive	amount=100.0 (100 L water)

Why Positive Values for Inputs?

If you're familiar with LCA matrix mathematics, you might expect inputs to be negative (since they're consumed). Here's why EcoSemantic uses positive values.

Understanding the Two-Level Convention

LCA software operates at two distinct levels:

graph TB
    subgraph "User/Data Level"
        A[User enters: amount = 5.0<br/>type = technosphere]
    end

    subgraph "EcoSemantic/Brightway2"
        B[Recognizes technosphere type]
        C[Applies sign transformation]
    end

    subgraph "Matrix Level"
        D[Matrix cell = -5.0]
    end

    A --> B
    B --> C
    C --> D

    style A fill:#e8f5e9
    style D fill:#fff3e0

Level 1: User/Data Level : How practitioners enter and think about data. This is what you interact with in EcoSemantic.

Level 2: Matrix Level
: How the calculation engine represents data mathematically. This is handled automatically.

The Matrix Convention

At the matrix level, the technosphere matrix follows the mathematical convention:

• Positive values = Production (outputs)
• Negative values = Consumption (inputs)

This is expressed in the fundamental LCA equation:

$$ \mathbf{s} = \mathbf{A}^{-1}\mathbf{f} $$

Where:

• $\mathbf{A}$ is the technosphere matrix
• $\mathbf{f}$ is the final demand vector
• $\mathbf{s}$ is the scaling vector

Why the Abstraction?

At the user level, most LCA software (including Brightway2, which powers EcoSemantic) uses positive values for inputs because:

1. It's more intuitive - "I need 5 kg of steel" not "I need -5 kg of steel"
2. Reduces errors - Less confusion about when to use negative signs
3. Matches data sources - ecoinvent and other databases show positive input values
4. Software handles conversion - The sign flip is automatic and consistent

How Brightway2 Handles This

When you create an exchange in EcoSemantic:

# What you specify:
amount = 5.0
exchange_type = "technosphere"

Brightway2's matrix builder automatically:

1. Recognizes this is a "technosphere" type exchange (consumption)
2. Applies sign transformation when building the technosphere matrix
3. Places -5.0 in the appropriate matrix cell

This behavior is documented in Brightway2's official documentation:

Brightway2 Documentation

"Include consumption edges but multiply the amount times negative one, to get the right sign in the technosphere matrix"

— Brightway2 Matrix Construction

Exchange Type Rules

Brightway2 applies different rules based on exchange type:

Exchange Type	Matrix Behavior
production	Value entered directly (no sign change)
substitution	Value entered directly (no sign change)
technosphere	Value multiplied by -1 (sign flipped)
biosphere	Value entered directly (no sign change)

Consistency with ecoinvent

This convention is fully consistent with how data is stored in the ecoinvent database. When you browse ecoinvent datasets:

• Input amounts are shown as positive values
• Production amounts are shown as positive values
• The database structure handles the mathematical transformation

EcoSemantic maintains this same user-facing convention to ensure:

• Seamless integration with ecoinvent data
• Familiar experience for LCA practitioners
• Consistent behavior across all tools

Practical Examples

Example 1: Simple Manufacturing Process

A process that produces 1 kg of plastic pellets, consuming electricity and emitting CO₂:

Activity: "Plastic pellet production"
Unit: kilogram
Location: GLO

Exchanges:
  # Reference product (what we produce)
  - name: "Plastic pellets"
    amount: 1.0          # ✅ Positive - production
    type: production

  # Electricity input
  - amount: 2.5          # ✅ Positive - consumed input
    type: technosphere
    input: "market for electricity, low voltage"

  # CO₂ emission  
  - amount: 1.8          # ✅ Positive - emission
    type: biosphere
    input: "Carbon dioxide, fossil"

Example 2: Recycling with Avoided Burden

A recycling process that avoids virgin material production:

Activity: "Steel recycling"
Unit: kilogram
Location: DE

Exchanges:
  # Reference product (recycled steel)
  - name: "Recycled steel"
    amount: 1.0          # ✅ Positive - production
    type: production

  # Scrap steel input
  - amount: 1.05         # ✅ Positive - consumed input
    type: technosphere
    input: "market for scrap steel"

  # Avoided virgin steel (credit)
  - amount: -0.9         # ⚠️ Negative - avoided burden
    type: technosphere
    input: "steel production, converter"

When to Use Negative Values

The avoided virgin steel has a negative amount because it represents a credit - the environmental burden that is avoided by using recycled material instead of virgin production.

Example 3: Multi-Input Manufacturing

A more complex process with multiple inputs:

Activity: "Electric motor production"
Unit: unit
Location: CN

Exchanges:
  # Reference product
  - name: "Electric motor, 10kW"
    amount: 1.0          # ✅ Positive
    type: production

  # Material inputs (all positive)
  - amount: 15.0         # ✅ 15 kg copper
    type: technosphere
    input: "market for copper"

  - amount: 25.0         # ✅ 25 kg steel  
    type: technosphere
    input: "market for steel, low-alloyed"

  - amount: 5.0          # ✅ 5 kg aluminum
    type: technosphere
    input: "market for aluminum"

  # Energy input
  - amount: 50.0         # ✅ 50 kWh electricity
    type: technosphere
    input: "market for electricity, medium voltage"

  # Emissions
  - amount: 0.5          # ✅ 0.5 kg VOC emissions
    type: biosphere
    input: "NMVOC, non-methane volatile organic compounds"

Common Mistakes to Avoid

❌ Wrong: Negative Values for Regular Inputs

# DON'T DO THIS - This is incorrect!
create_database_exchange(
    amount=-5.0,              # ❌ Wrong sign
    exchange_type="technosphere",
    input_activity_code="steel_code"
)

This would result in a positive value in the matrix, representing production instead of consumption. Your LCA results would be wrong.

✅ Correct: Positive Values for Regular Inputs

# DO THIS - This is correct!
create_database_exchange(
    amount=5.0,               # ✅ Correct sign
    exchange_type="technosphere",
    input_activity_code="steel_code"
)

❌ Wrong: Assuming Matrix-Level Convention

Don't try to "help" the software by pre-applying the negative sign:

# DON'T DO THIS
# "I know inputs should be negative in the matrix, so I'll use -5"
amount = -5.0  # ❌ Wrong thinking!

The exchange_type field tells Brightway2 how to handle the value. Trust the system.

EcoSemantic's Warning System

To help prevent mistakes, EcoSemantic includes a warning system that alerts you when negative values are used:

{
  "id": "exchange-uuid",
  "amount": -5.0,
  "exchange_type": "technosphere",
  "warning": "NEGATIVE AMOUNT DETECTED: You specified a negative value..."
}

This warning:

• ✅ Does not block the exchange creation
• ✅ Allows legitimate credit/recycling scenarios
• ✅ Alerts you to potential mistakes
• ✅ Can be ignored if the negative value is intentional

Technical Deep Dive

For those interested in the mathematical details, here's how the computation works.

The Technosphere Matrix

The technosphere matrix $\mathbf{A}$ represents the industrial economy:

• Rows = Products (goods and services)
• Columns = Processes (activities)
• Diagonal elements = Production amounts (typically positive)
• Off-diagonal elements = Consumption amounts (typically negative)

Matrix Construction

When Brightway2 constructs the matrix from your exchange data:

# Simplified pseudocode of what Brightway2 does internally
for exchange in activity.exchanges:
    if exchange.type == "production":
        # Enter value directly
        matrix[product_row, process_col] = exchange.amount
    elif exchange.type == "technosphere":
        # Flip the sign for consumption
        matrix[product_row, process_col] = -exchange.amount
    elif exchange.type == "biosphere":
        # Enter in biosphere matrix directly
        biosphere_matrix[flow_row, process_col] = exchange.amount

The LCA Calculation

The Life Cycle Inventory (LCI) calculation solves:

$$ \mathbf{s} = \mathbf{A}^{-1}\mathbf{f} $$

Then the Life Cycle Impact Assessment (LCIA) applies characterization:

$$ \mathbf{h} = \mathbf{C} \cdot \mathbf{B} \cdot \mathbf{s} $$

Where:

• $\mathbf{C}$ = Characterization matrix
• $\mathbf{B}$ = Biosphere matrix
• $\mathbf{s}$ = Scaling vector from LCI

References

• Brightway2 Documentation - Matrix Construction
• Brightway2 Documentation - Inventory Theory
• ecoinvent Methodology
• Heijungs, R., & Suh, S. (2002). The Computational Structure of Life Cycle Assessment. Springer.