tokens: test the stability of our reconstruction and the sensitivity of the model to various free parameters, we have considered different combinations of parameters. In particular, we either fixed , B sat, n , and c e as listed in Table 1 , or let them be free parameters within ranges 0.2–0.8, 50–850, and 0.2–0.5, respectively. These tests showed that the resulting reconstructions of TSI differed by up to 0.1 W m −2 on decadal timescales. The overall secular change always lies in the range 0.90–1.0 W m −2 . Consequently, we conclude that the reconstruction is independent of the exact choice of the free parameters (see also Krivova et al. 2007 ; Dasi-Espuig et al. 2016 ). 3.3. SATIRE-M reconstruction on millennial timescales Keeping all the parameters fixed, we now employ the SATIRE-M model to reconstruct solar total and spectral irradiance back to 6755 BC from the cosmogenic isotope data. Figure 7 a shows the TSI reconstructions over approximately the last 9000 years based on the three isotope series, as introduced in Sect. 2.3 (U16-14C in blue, U16-10Be in green, Wu18 in black). Figures 7 b and c are enlargements over the periods 1000 BC–2000 AD and 1400 AD–2000 AD, respectively. The decadally averaged TSI reconstruction based on the SN v2 series is also shown (solid red) for comparison. The reconstruction based on the sunspot record by Chatzistergos et al. (2017) is shown by the dashed red curve. Yellow shading highlights the difference between these two reconstructions. Fig. 7. Three TSI reconstructions based on different isotope records: U16-14C (blue), U16-10Be (green) and the composite Wu18 (black) plotted over the periods: panel a) 6755 BC–2000 AD, panel b) 1000 BC–2000 AD, and panel c) 1400 AD–2000 AD. The uncertainty range of the reconstruction based on the Wu18 composite is indicated by the grey shaded area. Decadal averages of the reconstruction based on the directly observed SN are shown in red after 1639. The solid line is the reconstruction based on the WDC-SILSO series while the dashed line is based on the record by Chatzistergos et al. (2017) . The yellow shaded area highlights the difference between them. It is worth noticing that the reconstructions based solely on either 14 C (U16-14C) or 10 Be (U16-10Be) show temporal discrepancies due to differences in the relevant geochemical production processes and local climatic influences (Sect. 2.3.1 and Wu et al. 2018 ). The reconstruction based on the composite (Wu18) of one global 14 C and six regional 10 Be series has remedied this (see Fig. 12 in Wu et al. 2018 ), and shows the common solar signal extracted from seven individual isotope series. We therefore consider this latter reconstruction to be more robust than reconstructions based on individual isotope data. On the millennial timescale, the variability of TSI () obtained from all three isotope records is very similar (≈0.11%). Since in the second half of the twentieth century, the activity of the Sun was comparatively high (see
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