1. Logarithmic effect of CO₂ • The warming effect of carbon dioxide grows logarithmically with concentration, not linearly. • This means the first 100 ppm of CO₂ caused a much larger temperature impact than, say, an increase from 400 → 500 ppm. • Each additional molecule of CO₂ contributes less extra warming because much of the infrared spectrum it absorbs is already saturated.

2. Geometry of “forcing” • Scientists describe this as radiative forcing, measured in watts per square meter. • Roughly, each doubling of CO₂ concentration produces about +3.7 W/m² of forcing, which translates (with climate sensitivity) to ~1.5–4.5°C warming. • So it takes geometrically more CO₂ to achieve each additional degree of warming. For example: • Going from 280 → 400 ppm may give ~1°C warming. • Going from 400 → 560 ppm (another 160 ppm) gives another ~1°C. • Going from 560 → 840 ppm (280 ppm more) gives another ~1°C. • And so on — the increments needed get larger each time.