  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 K (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 K. The temperature rise from 1820-1950 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 K and 1.9 +- 0.3
K, respectively.
