The Kaya identity, a core tool of sustainability science (used by the IPCC to structure emissions scenarios), factors total CO2 emissions into four measurable drivers:
CO2 = P × (GDP/P) × (E/GDP) × (CO2/E)
= Population × Affluence × Energy intensity × Carbon intensity
Each driver here compounds every simulated year as x(t) = x0 · (1+r)^t. The four colored bars in the 3D tower are the four factors on a shared height scale (index = 100 at year 0); the glowing tower on the right is their running product — total emissions. Because the identity is a pure product, taking the log turns growth into a sum:
d(ln CO2)/dt ≈ r_P + r_A + r_E + r_C
"Decoupling" is achieved whenever the negative rates (falling energy and carbon intensity, from efficiency and clean energy) outpace the positive rates (population and affluence growth) — the net rate readout turns green and the emissions tower starts shrinking even while GDP keeps rising.
- Population / GDP per capita — the scale drivers; historically almost always positive.
- Energy intensity (E/GDP) — efficiency: how much energy each unit of output needs.
- Carbon intensity (CO2/E) — the energy mix: how much CO2 each unit of energy emits.
- Paris-aligned preset — loads rates roughly consistent with a 1.5-2°C pathway, where intensity declines outrun growth.