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        A New Calibrated Sunspot Group Series Since 1749: Statistics of Active Day Fractions

        Usoskin, I. G.,Kovaltsov, G. A.,Lockwood, M.,Mursula, K.,Owens, M.,Solanki, S. K. D. Reidel Pub. Co 2016 Solar physics Vol.291 No.9

        <P>Although sunspot-number series have existed since the mid-nineteenth century, they are still the subject of intense debate, with the largest uncertainty being related to the 'calibration' of the visual acuity of individual observers in the past. A daisy-chain regression method is usually applied to inter-calibrate the observers, which may lead to significant bias and error accumulation. Here we present a novel method for calibrating the visual acuity of the key observers to the reference data set of Royal Greenwich Observatory sunspot groups for the period 1900 - 1976, using the statistics of the active-day fraction. For each observer we independently evaluate their observational thresholds [SS] defined such that the observer is assumed to miss all of the groups with an area smaller than SS and report all the groups larger than SS. Next, using a Monte-Carlo method, we construct a correction matrix for each observer from the reference data set. The correction matrices are significantly nonlinear and cannot be approximated by a linear regression or proportionality. We emphasize that corrections based on a linear proportionality between annually averaged data lead to serious biases and distortions of the data. The correction matrices are applied to the original sunspot-group records reported by the observers for each day, and finally the composite corrected series is produced for the period since 1748. The corrected series is provided as supplementary material in electronic form and displays secular minima around 1800 (Dalton Minimum) and 1900 (Gleissberg Minimum), as well as the Modern Grand Maximum of activity in the second half of the twentieth century. The uniqueness of the grand maximum is confirmed for the last 250 years. We show that the adoption of a linear relationship between the data of Wolf and Wolfer results in grossly inflated group numbers in the eighteenth and nineteenth centuries in some reconstructions.</P>

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        Solar activity over nine millennia: A consistent multi-proxy reconstruction

        Wu, C. J.,Usoskin, I. G.,Krivova, N.,Kovaltsov, G. A.,Baroni, M.,Bard, E.,Solanki, S. K. Springer-Verlag 2018 Astronomy and astrophysics Vol.615 No.-

        <P><I>Aims.</I> The solar activity in the past millennia can only be reconstructed from cosmogenic radionuclide proxy records in terrestrial archives. However, because of the diversity of the proxy archives, it is difficult to build a homogeneous reconstruction. All previous studies were based on individual, sometimes statistically averaged, proxy datasets. Here we aim to provide a new consistent multi-proxy reconstruction of the solar activity over the last 9000 yr, using all available long-span datasets of <SUP>10</SUP>Be and <SUP>14</SUP>C in terrestrial archives.</P><P><I>Methods.</I> A new method, based on a Bayesian approach, was applied for the first time to solar activity reconstruction. A Monte Carlo search (using the <I>χ</I><SUP>2</SUP> statistic) for the most probable value of the modulation potential was performed to match data from different datasets for a given time. This provides a straightforward estimate of the related uncertainties. We used six <SUP>10</SUP>Be series of different lengths (from 500-10 000 yr) from Greenland and Antarctica, and the global <SUP>14</SUP>C production series. The <SUP>10</SUP>Be series were resampled to match wiggles related to the grand minima in the <SUP>14</SUP>C reference dataset. The stability of the long data series was tested.</P><P><I>Results.</I> The Greenland Ice-core Project (GRIP) and the Antarctic EDML (EPICA Dronning Maud Land) <SUP>10</SUP>Be series diverge from each other during the second half of the Holocene, while the <SUP>14</SUP>C series lies in between them. A likely reason for the discrepancy is the insufficiently precise beryllium transport and deposition model for Greenland, which leads to an undercorrection of the GRIP series for the geomagnetic shielding effect. A slow 6-7 millennia variability with lows at ca. 5500 BC and 1500 AD in the long-term evolution of solar activity is found. Two components of solar activity can be statistically distinguished: the main component, corresponding to the “normal” moderate level, and a component corresponding to grand minima. A possible existence of a component representing grand maxima is indicated, but it cannot be separated from the main component in a statistically significant manner.</P><P><I>Conclusions.</I> A new consistent reconstruction of solar activity over the last nine millennia is presented with the most probable values of decadal sunspot numbers and their realistic uncertainties. Independent components of solar activity corresponding to the main moderate activity and the grand-minimum state are identified; they may be related to different operation modes of the dynamo.</P>

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