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The correlation between the averaged reconstructed March temperature record for Kyoto, Japan, and the reconstructed Total Solar Irradiance (TSI) over 660 years from 1230 to 1890 gives evidence with 98% probability that the  Little Ice Age  with four cold periods is forced by variations of TSI. If the correlation is restricted to the period 1650–1890, with two cold periods in the 17th and 19th century and for which two independent reconstructed March temperature records are available, the probability of solar forcing increases to 99.99%. As solar irradiance variations have a global effect there has to be a global climatic solar forcing impact. However, by how much global temperature were lower during these minima and with what amplitude TSI was varying is not accurately known. The two quantities, global temperature and TSI, are linked by the energy equilibrium equation for the Earth system. The derivation of this equation with respect to a variation of the solar irradiance has two terms: A direct forcing term, which can be derived analytically and quantified accurately from the Stefan-Boltzmann law, and a second term, describing indirect influences on the surface temperature. If a small TSI variation should force a large temperature variation, then it has to be the second indirect term that strongly amplifies the effect of the direct forcing. The current knowledge is summarized by three statements:   During the minima periods in the 13th, 15/16th, 17th, and 19th centuries the terrestrial climate was colder by 0.5–1.5 °C;    Indirect Top-down and Bottom-up mechanisms do not amplify direct forcing by a large amount, i.e. indirect solar forcing is of the same magnitude (or smaller) as direct solar forcing;    The radiative output of the Sun cannot be lower by more than 2 Wm −2  below the measured present-day TSI value during solar cycle minimum.   These three statements contradict each other and it is concluded that at least one is not correct. Which one is a wrong statement is presently not known conclusively. It is argued that it is the third statement and it is speculated that over centennial time scales the Sun might vary its radiance significantly more than observed so far during the last 40 years of space TSI measurements. To produce Maunder minimum type cold climate excursions, a TSI decrease of the order of 10 Wm −2  is advocated.

Changes in the Total Solar Irradiance and climatic effects