Current estimates of the impact of an increase in greenhouse gas concentrations on global warming, including by the IPCC and in General Circulation Models, are based on radiative forcing. Two recently published formulations of the theoretical foundation for radiative forcing are reviewed. Radiative forcing at the tropopause is calculated by assuming that the absorption of terrestrial radiation by greenhouse gases is determined by their spectral properties, using a radiative transmittance function based on the line strength and line shape of the absorption lines and the vertical optical mass, whilst, under conditions of local thermodynamic equilibrium, the emission of radiation at each layer of the atmosphere is given by the Planck blackbody function at the local atmospheric temperature. Radiative forcing is given by the net change in radiative flux at the troposphere due to an increase in greenhouse gases. Climate change is seen to take place when the system responds to restore the radiative equilibrium. Without any theoretical foundation, a linear relationship between the change in surface temperature in °C and radiative forcing is assumed. Here, IPCC 2013’s estimate of radiative forcing of 2.83 W/m2 due to the increase in greenhouse gases from 1750 to 2011 is used to calculate the resulting change in radiative flux at the Earth’s surface under reasonable assumptions, and the Stefan-Boltzmann law is applied to calculate the change in surface temperature of between 0.8 and 1.0 °C. This represents a climate sensitivity of around 0.32 °C/(W/m2), about one third of the climate sensitivity of 1.0 °C/(W/m2) used by IPCC 2013 that was obtained from the mean regression-based values of 30 climate models.

Examination of the radiation budget at the surface of the Earth shows that there are three factors affecting the surface temperature; the amount of solar radiation absorbed by the atmosphere and by the surface respectively, and the amount of leakage of infrared radiation emitted from the surface directly into space. If there were no leakage, the upwelling infrared radiation from the Earth’s surface would be equal to the incoming solar radiation absorbed by the atmosphere plus twice the solar radiation absorbed by the surface. This results from the summation of a sequence of equal upward and downward re-emissions of infrared radiation absorbed by the atmosphere following the initial absorption of solar radiation. At current levels of solar absorption, this would result in total upwelling radiation of approximately 398.6 W/m2, or a maximum surface temperature of 16.4°C. Allowing for leakage of infrared radiation through the atmospheric window, the resulting emission from the Earth’s surface is reduced to around 396 W/m2, corresponding to the current average global surface temperature of around 15.9°C. Absorption of solar and infrared radiation by greenhouse gases is determined by the absorption bands for the respective gases and their concentrations. Absorption of incoming solar radiation is largely by water vapor and ozone, and an increase in absorption would reduce not increase the surface temperature. Moreover, it is probable that all emitted infrared radiation that can be absorbed by greenhouse gases, primarily water vapor, with a small contribution from carbon dioxide and ozone, is already fully absorbed, and the leakage of around 5.5 % corresponds to the part of the infrared red spectrum that is not absorbed by greenhouse gases. The carbon dioxide absorption bands, which represent a very small percentage of the infrared spectrum, are most likely fully saturated. In these circumstances, increased concentrations of greenhouse gases, and carbon dioxide in particular, will have no effect on the emitted radiation. The surface temperature is probably at the thermodynamic limit for the current luminosity of the sun. Satellite based measurements since 1979 suggest that any global warming over the past 150 years may be due to an increase in total solar irradiance, which we are still a decade or two from being able to confirm.

Paleo and recent sea surface temperature (SST) measurements at six locations spanning the North Atlantic, from the northeastern North Atlantic off the British Isles to the Dry Tortugas in the southwest, were examined in order to determine whether a period of cooling was responsible for the die-off of elkhorn corals (Acropora palmata) on the reef off Broward County around six thousand years ago (6 Kya) and whether warming sea temperatures might contribute to their recovery. The paleo data show indications of a warm period between 13 Kya and 7 Kya, followed by cooling, probably due to orbital forcing arising from the coincidence of insolation maxima in the Milankovitch obliquity and axial precession cycles in the Northern hemisphere at that time, but the lack of paleo data in the immediate proximity of the reef makes it difficult to draw firm conclusions regarding the die-off of the corals. However, the marine SST data obtained from ships and buoys since 1870 raise questions about the presumed recent global warming. Annual average sea surface temperatures in the North Atlantic show remarkable stability and consistency with little or no change over the 146 years between 1870 and 2015, despite large seasonal and latitudinal variation in response to differences in solar irradiance.