The radiative forcing from carbon dioxide is approximately logarithmic in its concentration, producing about four watts per square meter of global-mean forcing for each doubling. Although these are basic facts of climate science, competing explanations for them have been given in the literature. Here, the reasons for the logarithmic forcing of carbon dioxide are explored in detail and a simplified model for the forcing is constructed. An essential component is the particular distribution of absorption coefficients within the 15-micron band of carbon dioxide. An alternative explanation, which does not depend on the spectrum of carbon dioxide, but hinges on the tropospheric lapse rate instead, is shown to be neither necessary nor sufficient to explain the logarithmic forcing of carbon dioxide and to be generally inapplicable to well-mixed greenhouse gases in Earth’s atmosphere.

Jacob P. (2022-07-01). "Why the Forcing from Carbon Dioxide Scales as the Logarithm of Its Concentration". Journal of Climate. 35 (13): 4027–4047. Bibcode:2022JCli Radiative forcing (or climate forcing) is a concept used to quantify a change to the balance of energy flowing through a planetary atmosphere. Various factors contribute to this change in energy balance, such as concentrations of greenhouse gases and aerosols, and changes in surface albedo and solar irradiance. In more technical terms, it is defined as "the change in the net, downward minus upward The atmospheric burden of greenhouse gases due to human activity has grown especially rapidly during the last several decades (since about year 1950). For carbon dioxide, the 50% increase (C/C0 = 1.5) realized as of year 2020 since 1750 corresponds to a cumulative radiative forcing change (delta F) of +2.17 W/m2. Assuming no change in the emissions growth path, a doubling of concentrations (C/C0 = 2) within the next several decades would correspond to a cumulative radiative forcing change (delta F) of +3.71 W/m2. The relationship between CO2 and radiative forcing is logarithmic at concentrations up to around eight times the current value. Constant concentration increases thus have a progressively smaller warming effect. However, the first-order approximation is inaccurate at higher concentrations and there is no saturation in the absorption of infrared radiation by CO2. Various mechanism behind the logarithmic scaling has been proposed but the spectrum distribution of the carbon dioxide seems to be essential, particularly a broadening in the relevant 15-μm band coming from a Fermi resonance present in the molecule.

increased concentrations of water vapor in the atmosphere, also contribute to climate change. The warming from the greenhouse effect has a logarithmic relationship The scientific community has been investigating the causes of current climate change for decades. After thousands of studies, the scientific consensus is that it is "unequivocal that human influence has warmed the atmosphere, ocean and land since pre-industrial times." This consensus is supported by around 200 scientific organizations worldwide. The scientific principle underlying current climate The scientific community has been investigating the causes of current climate change for decades. After thousands of studies, the scientific consensus is that it is "unequivocal that human influence has warmed the atmosphere, ocean and land since pre-industrial times." This consensus is supported by around 200 scientific organizations worldwide. The scientific principle underlying current climate change is the greenhouse effect, which provides that greenhouse gases pass sunlight that heats the earth, but trap some of the resulting heat that radiates from the planet's surface. Large amounts of greenhouse gases such as carbon dioxide and methane have been released into the atmosphere through burning of fossil fuels since the industrial revolution. Indirect emissions from land use change, emissions of other greenhouse gases such as nitrous oxide, and increased concentrations of water vapor in the atmosphere, also contribute to climate change. The warming from the greenhouse effect has a logarithmic relationship with the concentration of greenhouse gases.…