M8: Dynamic MFA and stock dynamics

Question 1

Why do we need time-dependent models in MFA?

Answer 1

Because actions often have delayed consequences (good or bad)
- Example: Carbon emissions –> Global Warming

Question 2

In which scenarios may a stationary (or quasi-stationary) model be sufficient?

Answer 2

• If the system behaves linearly (e.g. no stock changes)

- If we are interested only in a short time period (e.g. one year)

Question 3

When is a dynamic model necessary?

Answer 3

• If we want to analyze change or understand when the effects of actions may occur.

Question 4

What are dynamic MFA models?

Answer 4

Time-dependent or dynamic models are developed in the same way as stationary or quasi-stationary models.

The difference is that system variables and system parameters are not individual numbers, but functions of time.

Question 5

Mention the three types of time-dependent models

Answer 5

1. Discrete, given time series (of quasi-stationary models)
   - -> fx historic nitrogen emissions to water
2. Discrete model approach (difference equations)
3. Continuous model approach (differential equations)

Question 6

What does it require to make dynamic models of the future?

Answer 6

It requires hypotheses about what governs change.

• -> such hypotheses can usually not be proven correct (e.g. growth rates may change).
• -> but hypotheses can be tested using historic data

Question 7

What are the limitations of exponential growth models?

Answer 7

Population continues to grow unlimited over time (unconstrained)

Unrealistic for most populations if long time periods are analyzed

• assumes unlimited resources
• assumes unlimited space
• assumes no competition

Examples for predictions using exponential growth:

• Thomas R. Malthus (1798): An Essay on the Principle of Population
• Club of Rome (1972): Limits to Growth

Question 8

What are the limitations of logistic growth?

Answer 8

• Assumes stable condition for saturation
–> growth slows down smoothly once population reaches carrying capacity

• Might be very unrealistic if environment becomes unstable
–> might have dramatic impacts on population changes

• Carrying capacity K is difficult to determine
–> might even change as conditions change

Question 9

Waste flows are often difficult to measure or entirely unknown.
How can we model waste flows?

Answer 9

1. Leaching approach
   –> output as a fraction of the stock
   (here the stock needs to be known and the approach is suitable for diffuse emissions but only suitable for solid waste if the stock is constant)
2. Lifetime approach
   –> output as a delayed input
   (here we need to know the inputs)

Question 10

In which two ways can material stocks be detemined?

Answer 10

a) ‘bottom-up’: from building and vehicle statistics and product-specific material content data
b) ‘top-down’: from aggregated consumption data and a lifetime model

Question 11

How can one build scenarios for the future development of material cycles?

Answer 11

• Extrapolate or assume future consumption levels and then calculate the stocks and the services provided.
• Extrapolate or assume future service levels, infer the stocks required to deliver them, and calculate the inflows required to expand and maintain those stocks.

Question 12

What question does the stock-driven model answer?

Answer 12

How large is the inflow needed to maintain and expand the in-use stock so that it fits a given scenario?

Question 13

What is a stock-driven model?

Answer 13

The stock-driven model is the inverse of the inflow driven model:
• The inflow computed by the stock-driven model is identical to the original inflow.
• The stock computed with the inflow-driven model is identical to the original stock.

Be creative with the initial stock!
• Use stock obtained from inflow-driven model to apply stock-driven model from a time when there were virtually no stocks.
• If the original stock age-cohort composition is unknown, the leaching model can be applied to S0.