Uncertainty and Systems Analysis
Systems and Uncertainty
Deterministic systems models can be subject to uncertainties due to the separation between the “internals” of the system and the “external” environment.
Reminder: “All Models Are Wrong, But Some Are Useful”
Every systems model simplifies or neglects certain aspects of the system!
Even if appropriate, this results in uncertainty about how results translate to the real system.
What is Uncertainty?
Glib Answer: A lack of certainty!
More Seriously: Uncertainty refers to an inability to exactly describe current or future values or states.
Types of Uncertainty
Two (broad) types of uncertainties:
- Aleatory uncertainty, or uncertainties resulting from randomness;
- Epistemic uncertainty, or uncertainties resulting from lack of knowledge.
Probability
We often represent uncertainty using probabilities.
What is probability?
Two Definitions of Probability
- Long-run frequency of an event (frequentist)
- Degree of belief that a proposition is true (Bayesian)
The frequentist definition concerns what would happen with a large enough number of repeated trials.
The Bayesian definition concerns the odds that you should bet on an outcome.
Probability Distributions
We often represent probability using distributions — more on this next time.
The choice of distributions can often play a large role in outcomes.
Neglecting Correlations
For example, an often key concern is whether uncertainties are correlated: do certain outcomes tend to occur in combination?
If this is the case, it can bias results to assume independence.
Climate Change
Let’s look at how global mean temperatures have changed from 1850–2022 relative to a preindustrial baseline.
Causes of Climate Changes
Climatic changes result from changes to the heat or energy balance of the Earth due to alterations to the chemical composition of the atmosphere, which include:
- greenhouse gas emissions;
- aerosol emissions from air pollution or volcanic eruptions;
- changes to the solar cycle.
Radiative Forcing
The impact of these changes on the energy balance of the planet are referred to as radiative forcing.
A positive radiative forcing means a warming effect (net heat increase) and a negative radiative forcing means a cooling effect (net heat loss).
Projections of Future Radiative Forcing
Let’s look at the projected forcings from one of the official scenarios (actually the most extreme scenario) used to assess future climate change.
What Is Uncertain?
There are many uncertainties in modeling climate changes:
- How much CO2 gets absorbed by sinks/emitted by sources?
- How strong is the aerosol cooling effect?
- How rapidly is heat absorbed by and transported into the deep ocean?
- What is the atmospheric temperature response to increases in radiative forcing?
Impact of Neglecting Climate Correlations
Neglecting these correlations can change the distribution of hindcasted and projected temperatures.
