Separate Climate Emulator Sensitivity from Attribution

5 questions0m 0s

Prerequisites

Partial derivatives, interaction terms, model calibration, and causal reasoning.

Learn the skill

In an emulator, a partial derivative holds other inputs fixed. Interaction terms make marginal sensitivity depend on the reference state. An algebraic decomposition of model output is not automatically a causal attribution in the physical world.

Worked example

For Y = aX + bZ + cXZ, dY/dX = a + cZ. Finite changes involving both inputs contain an interaction contribution whose allocation depends on a declared convention.

Model and Assumptions

Use the invented dimensionless climate emulator T = 2C + A + CA, where C and A are centered input indices, not measured concentrations. Compare baseline (C,A)=(0,0) with (1,1). This toy model is not a forecast or a calibrated attribution study.

1. What is T at (1,1)? Answer

2. What is the partial derivative of T with respect to C at A=1? Answer

3. If C changes first from the baseline, how much does that step add? 2 3 4

4. If A changes first, how much does the later C step add? 2 1 3

5. What does the order dependence reveal? One input has no role A convention is needed to allocate the interaction The total change depends on arithmetic order

Further inquiry

Compute both order-based allocations and their equal-order average. Then explain which physical and causal assumptions would be needed before using this emulator for real-world attribution.

Review criteria

Report average contributions of 2.5 for C and 1.5 for A.
Distinguish a chosen allocation rule from physical identification.
Discuss calibration, counterfactual validity, and omitted drivers.

Research notes (not saved or graded)