A fractal climate response function can simulate global average temperature trends of the modern era and the past millennium

A climate response function is introduced that consists of six exponential (low-pass) filters with weights depending as a power law on their e-folding times. The response of this two-parameter function to the combined forcings of solar irradiance, greenhouse gases, and SO2-related aerosols is fitted simultaneously to reconstructed temperatures of the past millennium, the response to solar cycles, the response to the 1991 Pinatubo volcanic eruption, and the modern 1850–2010 temperature trend. Assuming strong long-term modulation of solar irradiance, the quite adequate fit produces a climate response function with a millennium-scale response to doubled CO2 concentration of 2.0 ± 0.3 °C (mean ± standard error), of which about 50 % is realized with e-folding times of 0.5 and 2 years, about 30 % with e-folding times of 8 and 32 years, and about 20 % with e-folding times of 128 and 512 years. The transient climate response (response after 70 years of 1 % yearly rise of CO2 concentration) is 1.5 ± 0.2 °C. The temperature rise from 1820 to 1950 can be attributed for about 70 % to increased solar irradiance, while the temperature changes after 1950 are almost completely produced by the interplay of anthropogenic greenhouse gases and aerosols. The SO2-related forcing produces a small temperature drop in the years 1950–1970 and an inflection of the temperature curve around the year 2000. Fitting with a tenfold smaller modulation of solar irradiance produces a less adequate fit with millennium-scale and transient climate responses of 2.5 ± 0.4 and 1.9 ± 0.3 °C, respectively.