Radiative forcing efficiency

One of the most surprising property of radiative forcing, in W/m2, is the variability of its efficiency , that is to say its impact on the Earth’s global temperature, in °C, depending on the periods. The application of the Stefan-Boltzmann law tells us that, if we consider that our planet behaves as a black body, that is to say, its emission spectrum in the infrared only depends on its temperature, the efficiency of solar forcing is 0.22 °C/(W/m2). Yet this efficiency can be increased considerably since climate archives teach us that it is up to 5 °C/(W/m2) in the band 73.7-147.5 Kyrs during the glacial-interglacial periods, a consequence of orbital forcing. On the other hand, equal to 1.5 °C/(W/m2) in the band 576-1152 years at the beginning of the Holocene because of solar forcing, it is 0.5 °C/(W/m2) nowadays.

Such a change in radiative forcing efficiency assumes a positive feedback loop in the climate system because the variability of the incident short wavelength radiation is far too low to impact overall temperature. To explain the resonant character of the climate system it is necessary to involve the oceans through the modulated response of subtropical gyres (Pinault, 2018d). The amplifying effect of solar and orbital forcing comes from the positive feedback exerted by the polar current of the gyral Rossby wave: the oscillation of the thermocline is amplified by the polar current which warms or cools, as the western boundary current accelerates or slows down. The amplification is tightly controlled because limited by the sea water’s ability to warm at low latitudes and by the resulting cooling of upwelling along the eastern boundary current of the gyre.

Thus, the amplifying effect of solar and orbital forcing shows that the transfer of heat from the equator to the poles occurs with varying efficiency. Acceleration or, conversely, slow-down of the polar current of the gyral Rossby wave impacts sea surface temperature anomalies, especially at high latitudes of the subtropical gyres. These thermal anomalies act either as a heat source, or, contrarily, as a heat sink. The resulting perturbation behaves like an isolated thermodynamic system: heat transfer between oceans and continents occur until equilibrium is established between the oceanic and continental anomalies.

The amplification phenomenon is all the more significant as the sea surface temperature at high latitudes is lower, which has the property to increase feedback. Thus the forcing efficiency depends on the forward motion of sea ice in both hemispheres, which explains its evolution during the Holocene. Regarding the orbital forcing whose bandwidth is narrow, its efficiency is highly dependent on the difference between the period of forcing and the natural period of the gyral Rossby wave. Thus in the period extending from 3.0 to 0.8 million years before our era, the period of 41,000 years predominates, corresponding to changes in the tilt of the earth. Over the past 800,000 years, the dominating period of oscillation of glacial – interglacial is 100,000 years, corresponding to changes in the eccentricity of the earth.