  Context. There is no consensus on the amplitude of the historical solar
forcing. The estimated magnitude of the total solar irradiance difference
between Maunder minimum and present time ranges from 0.1 to 6 W/m2 making
uncertain the simulation of the past and future climate. One reason for this
disagreement is the applied evolution of the quiet Sun brightness in the solar
irradiance reconstruction models. This work addresses the role of the quiet Sun
model choice and updated solar magnetic activity proxies on the solar forcing
reconstruction. Aims. We aim to establish a plausible range of the solar
irradiance variability on decadal to millennial time scales. Methods. The
spectral solar irradiance (SSI) is calculated as a weighted sum of the
contributions from sunspot umbra/penumbra, fac- ulae and quiet Sun, which are
pre-calculated with the spectral synthesis code NESSY. We introduce activity
belts of the contributions from sunspots and faculae and a new structure model
for the quietest state of the Sun. We assume that the brightness of the quiet
Sun varies in time proportionally to the secular (22-year smoothed) variation
of the solar modulation potential. Results. A new reconstruction of the TSI and
SSI covering the period 6000 BCE - 2015 CE is presented. The model simulates
solar irradiance variability during the satellite era well. The TSI change
between the Maunder and recent minima ranges between 3.7 and 4.5 W/m2 depending
on the applied solar modulation potential. The implementation of a new quietest
Sun model reduces, by approximately a factor of two, the relative solar forcing
compared to the largest previous estimation, while the application of updated
solar modulation potential increases the forcing difference between Maunder
minimum and the present by 25-40 %.
