Quote:The primary source of energy in the Earth’s climate system is incoming solar radiation, termed total solar irradiance, or TSI. At equilibrium, because of the requirement of energy conservation, the Earth’s radiative budget must balance such that TSI is equal to outgoing longwave radiation at the top of the atmosphere (a state known as radiative equilibrium). Since the radiation emitted by a body is a function of surface temperature, the Earth’s ‘effective temperature’ (TE) is the temperature at which radiative equilibrium is achieved assuming the Earth acts like a blackbody, and can be calculated (in K)
That is simple enough: at equilibrium, i.e. neither heating or cooling we need to radiate as much energy as we get from the sun at the top of the atmosphere.
In terms of geologic time, as the sun develops and grows warmer something must happen for the earth to not heat up. Not that the world is always at equilibrium, of course.
Quote:where Fs is the TSI (currently ∼1,368 Wm−2), σ is the Stefan–Boltzmann constant (5.67 × 10−8 W m−2 K−4), A=0.29 (ref. 1) is the Earth’s average planetary albedo (the fraction of incoming radiation scattered or reflected back out of the atmosphere by clouds, particulates in the atmosphere and the Earth’s surface), and the factor of 4 accounts for the spherical and rotating nature of the Earth. The 31 K difference between TE and the observed surface temperature of the Earth (+14.0 °C or 287.1 K is the 1961–1990 mean2) is almost entirely due to the action of the greenhouse effect
Quote:The majority (∼75%) of the greenhouse effect is due to the warming effects of water vapour and clouds, with the non-condensing greenhouse gasses (predominantly CO2 and CH4) accounting for the remaining 25% (ref. 3). However, at the temperatures and pressures typical of the Earth’s surface, water vapour and clouds act as feedbacks rather than drivers of the greenhouse effect, with CO2 and CH4, and the other non-condensing GHGs (for example, N2O) determining the overall strength of the greenhouse effect. Given this understanding, and that summarized in equation (1), the climatic evolution of the Earth over geological time is largely a function of the concentration of the non-condensing greenhouse gases, planetary albedo (A) and the TSI (Fs; for example, ref. 4).
As CO2 + CH4 warm the world more water is evaporated increasing the amount of water vapor in the atmosphere.
Quote:As a result, there has been an increase in TSI of ∼400 Wm−2 since the formation of the Earth.
We can explain now one of Ajax’ favorite tokens to ward off evil aka chart: in early Cambrian/Ordovician time the sun was much weaker than now. So, forgetting that chart we continue with the article.
Quote:Following ref. 4, and assuming an effective emissivity, ɛ, of the Earth of 0.6 (that is, 40% of longwave radiation is absorbed by greenhouse gases in the atmosphere), equation (1) can be used to define the following equation that describes S for today’s climate (where the surface temperature=287.1 K) in the absence of any climate feedbacks (for example, water vapour, sea-ice etc.), also known as the Planck response (hence the subscript ‘P’)
Following ref. 4, and assuming an effective emissivity, ɛ, of the Earth of 0.6 (that is, 40% of longwave radiation is absorbed by greenhouse gases in the atmosphere), equation (1) can be used to define the following equation that describes S for today’s climate (where the surface temperature=287.1 K) in the absence of any climate feedbacks (for example, water vapour, sea-ice etc.), also known as the Planck response (hence the subscript ‘P’) [/quote]

The triangles represent change in a variable, spoken as “delta” (Greek letter.)
Quote:SP depends on the overall strength of the greenhouse effect and the surface temperature of the Earth, and so this value is not necessarily applicable throughout Earth’s history; nonetheless, this treatment provides a first-order constraint that the long-term secular increase in TSI of 400 Wm−2 would be associated with a secular warming of at least ∼20 K over the last 4.5 billion years, if albedo and emissivity remained constant. Since the combined effect of the greenhouse gas and other climate feedbacks (for example, water vapour, lapse rate, sea-ice etc.) is positive8, this is a minimum estimate of S and when all climate feedbacks are considered, Sa (where ‘a’ denotes actuo after ref. 7) is likely in the range of 0.8– 1.6 K W−1 m2 (for example, refs 7, 9, 10, 11).
The actual evolution of Earth’s temperature through geological time is a subject of considerable debate (for example, ref. 12), yet there is a longstanding view that, despite the increase in solar output, Earth’s surface temperature was, for much of geological time, warmer, not colder, than today (for example, refs 13, 14). This apparent inconsistency is known as the ‘Faint Young Sun’ paradox and to reconcile the observation of a relatively stable climate in the face of increasing solar output through time requires a parallel change in some other factors that influence Earth’s radiative budget. First and foremost among these
cont’d