Final answer:
The response to a doubling of atmospheric CO₂ from pre-industrial levels is a predicted increase in global average temperature of about 3.0°C, due to the climate's sensitivity to radiative forcing. However, estimates range from 1.1°C to 6.4°C, reflecting uncertainties in the climate models.
Step-by-step explanation:
The question at hand is concerned with the increase in global average surface temperature in response to a doubling of CO₂ levels from pre-industrial times. Through the use of mathematical models, we understand that a doubling of CO₂ from pre-industrial levels of 280 ppm to 560 ppm would lead to a theoretical increase of about 3.0°C in global average temperature. This is assuming a climate sensitivity parameter of 0.8°C per W/m² of radiative forcing, which considers the various feedback mechanisms that are largely positive.
These mathematical models present a range of potential temperature increases due to the complexities in the Earth's carbon cycle and the uncertainties in climate feedbacks, with estimates varying from a 1.1°C to a 6.4°C rise. It's significant to note that the impact on temperature is not linear; as CO₂ levels rise, the warming effect increases logarithmically. Presently, we have already observed an increase of about 1.0°C due to the anthropogenic rise in greenhouse gases, indicating that the process of warming is well underway.