The Experts below are selected from a list of 5847 Experts worldwide ranked by ideXlab platform
Luke Barnard - One of the best experts on this subject based on the ideXlab platform.
-
tests of Sunspot Number sequences 4 discontinuities around 1946 in various Sunspot Number and Sunspot group Number reconstructions
Solar Physics, 2016Co-Authors: Mike Lockwood, M J Owens, Luke BarnardAbstract:We use five test data series to search for, and quantify, putative discontinuities around 1946 in five different annual-mean Sunspot-Number or Sunspot-group-Number data sequences. The data series tested are the original and new versions of the Wolf/Zurich/International Sunspot Number composite [ $R_{\text{ISNv1}}$ and $R_{\text{ISNv2}}$ ] (respectively Clette et al. in Adv. Space Res. 40, 919, 2007 and Clette et al. in The Solar Activity Cycle 35, Springer, New York, 2015); the corrected version of $R$ ISNv1 proposed by Lockwood, Owens, and Barnard (J. Geophys. Res. 119, 5193, 2014a) [ $R _{\mathrm{C}}$ ]; the new “backbone” group-Number composite proposed by Svalgaard and Schatten (Solar Phys. 291, 2016) [ $R_{\text{BB}}$ ]; and the new group-Number composite derived by Usoskin et al. (Solar Phys. 291, 2016) [ $R_{\text{UEA}}$ ]. The test data series used are the group-Number [ $N_{\mathrm{G}}$ ] and total Sunspot area [ $A _{\mathrm{G}}$ ] from the Royal Observatory, Greenwich/Royal Greenwich Observatory (RGO) photoheliographic data; the Ca K index from the recent re-analysis of Mount Wilson Observatory (MWO) spectroheliograms in the Calcium ii K ion line; the Sunspot-group-Number from the MWO Sunspot drawings [ $N_{\text{MWO}}$ ]; and the dayside ionospheric F2-region critical frequencies measured by the Slough ionosonde [foF2]. These test data all vary in close association with Sunspot Numbers, in some cases non-linearly. The tests are carried out using both the before-and-after fit-residual comparison method and the correlation method of Lockwood, Owens, and Barnard, applied to annual mean data for intervals iterated to minimise errors and to eliminate uncertainties associated with the precise date of the putative discontinuity. It is not assumed that the correction required is by a constant factor, nor even linear in Sunspot Number. It is shown that a non-linear correction is required by $R_{\mathrm{C}}$ , $R_{\mathrm{BB}}$ , and $R_{\text{ISNv1}}$ , but not by $R_{\text{ISNv2}}$ or $R_{\text{UEA}}$ . The five test datasets give very similar results in all cases. By multiplying the probability distribution functions together, we obtain the optimum correction for each Sunspot dataset that must be applied to pre-discontinuity data to make them consistent with the post-discontinuity data. It is shown that, on average, values for 1932 – 1943 are too low (relative to later values) by about 12.3 % for $R_{\text{ISNv1}}$ but are too high for $R_{\text{ISNv2}}$ and $R_{\mathrm{BB}}$ by 3.8 % and 5.2 %, respectively. The correction that was applied to generate $R_{\mathrm{C}}$ from $R$ ISNv1 reduces this average factor to 0.5 % but does not remove the non-linear variation with the test data, and other errors remain uncorrected. A valuable test of the procedures used is provided by $R_{\text{UEA}}$ , which is identical to the RGO $N_{\mathrm{G}}$ values over the interval employed.
-
tests of Sunspot Number sequences 2 using geomagnetic and auroral data
Solar Physics, 2016Co-Authors: Mike Lockwood, M J Owens, Luke Barnard, Chris J Scott, Heikki NevanlinnaAbstract:We compare four Sunspot-Number data sequences against geomagnetic and terrestrial auroral observations. The comparisons are made for the original Solar Influences Data Center (SIDC) composite of Wolf/Zurich/International Sunspot Number [ $R_{\text{ISNv}1}$ ], the group Sunspot Number [ $R_{\mathrm{G}}$ ] by Hoyt and Schatten (Solar Phys. 181, 491, 1998), the new “backbone” group Sunspot Number [ $R_{\mathrm{BB}}$ ] by Svalgaard and Schatten (Solar Phys., , 2016), and the “corrected” Sunspot Number [ $R_{\mathrm{C}}$ ] by Lockwood, Owens, and Barnard (J. Geophys. Res. 119, 5172, 2014a). Each Sunspot Number is fitted with terrestrial observations, or parameters derived from terrestrial observations to be linearly proportional to Sunspot Number, over a 30-year calibration interval of 1982 – 2012. The fits are then used to compute test sequences, which extend further back in time and which are compared to $R_{\text{ISNv}1}$ , $R_{\mathrm{G}}$ , $R_{\text{BB}}$ , and $R_{\mathrm{C}}$ . To study the long-term trends, comparisons are made using averages over whole solar cycles (minimum-to-minimum). The test variations are generated in four ways: i) using the IDV(1d) and IDV geomagnetic indices (for 1845 – 2013) fitted over the calibration interval using the various Sunspot Numbers and the phase of the solar cycle; ii) from the open solar flux (OSF) generated for 1845 – 2013 from four pairings of geomagnetic indices by Lockwood et al. (Ann. Geophys. 32, 383, 2014a) and analysed using the OSF continuity model of Solanki, Schussler, and Fligge (Nature, 408, 445, 2000), which employs a constant fractional OSF loss rate; iii) the same OSF data analysed using the OSF continuity model of Owens and Lockwood (J. Geophys. Res. 117, A04102, 2012), in which the fractional loss rate varies with the tilt of the heliospheric current sheet and hence with the phase of the solar cycle; iv) the occurrence frequency of low-latitude aurora for 1780 – 1980 from the survey of Legrand and Simon (Ann. Geophys. 5, 161, 1987). For all cases, $R_{\mathrm{BB}}$ exceeds the test terrestrial series by an amount that increases as one goes back in time.
-
tests of Sunspot Number sequences 4 discontinuities around 1946 in various Sunspot Number and Sunspot group Number reconstructions
arXiv: Solar and Stellar Astrophysics, 2016Co-Authors: Mike Lockwood, M J Owens, Luke BarnardAbstract:We use 5 test data series to quantify putative discontinuities around 1946 in 5 annual-mean Sunspot Number or group Number sequences. The series tested are: the original and new versions of the Wolf/Zurich/International Sunspot Number composite [$R_{ISNv1}$ and $R_{ISNv2}$] ; the corrected version of $R_{ISNv1}$ [$R_C$]; the backbone group Number [$R_{BB}$]; and the group Number composite [$R_{UEA}$]. The test data are: the group Number $N_G$ and total Sunspot area $A_G$ from the RGO photoheliographic data; the CaK index from re-analysis of MWO CaII K spectroheliograms; the group Number from the MWO Sunspot drawings, $N_{MWO}$; and ionospheric critical frequencies at Slough [$foF2$]. The test data all vary with Sunspot Numbers, in some cases non-linearly. Tests use both before-and-after fit-residual comparison and correlation methods, applied to intervals iterated to minimise errors and eliminate the effect of the discontinuity date. It is not assumed that the correction required is by a constant factor, nor even linear in Sunspot Number. A non-linear correction is required by $R_C$, $R_{BB}$ and $R_{ISNv1}$, but not by $R_{ISNv2}$ or $R_{UEA}$. The test datasets give very similar results in all cases. By multiplying the probability distribution functions together we obtain the optimum correction for each data series that must be applied to pre-discontinuity data to make them consistent with the post-discontinuity data. It is shown that, on average, values for 1932-1943 are too small (relative to later values) by about 12.3% for $R_{ISNv1}$ but are too large for $R_{ISNv2}$ and $R_{BB}$ by 3.8% and 5.2%. The correction applied to generate $R_C$ from $R_{ISNv1}$ reduces this average factor to 0.5% but does not remove the non-linear variation, and other errors remain uncorrected. A test is provided by $R_{UEA}$, which is identical to the RGO $N_G$ values over the interval used.
-
tests of Sunspot Number sequences 2 using geomagnetic and auroral data
arXiv: Solar and Stellar Astrophysics, 2016Co-Authors: Mike Lockwood, M J Owens, Luke Barnard, Chris J Scott, Heikki NevanlinnaAbstract:We compare four Sunspot-Number data sequences against geomagnetic and terrestrial auroral observations. The comparisons are made for the original SIDC composite of Wolf-Zurich-International Sunspot Number [$R_{ISNv1}$], the group Sunspot Number [$R_{G}$] by Hoyt and Schatten (Solar Phys., 1998), the new "backbone" group Sunspot Number [$R_{BB}$] by Svalgaard and Schatten (Solar Phys., 2016), and the "corrected" Sunspot Number [$R_{C}$] by Lockwood at al. (J.G.R., 2014). Each Sunspot Number is fitted with terrestrial observations, or parameters derived from terrestrial observations to be linearly proportional to Sunspot Number, over a 30-year calibration interval of 1982-2012. The fits are then used to compute test sequences, which extend further back in time and which are compared to $R_{ISNv1}$, $R_{G}$, $R_{BB}$, and $R_{C}$. To study the long-term trends, comparisons are made using averages over whole solar cycles (minimum-to-minimum). The test variations are generated in four ways: i) using the IDV(1d) and IDV geomagnetic indices (for 1845-2013) fitted over the calibration interval using the various Sunspot Numbers and the phase of the solar cycle; ii) from the open solar flux (OSF) generated for 1845 - 2013 from four pairings of geomagnetic indices by Lockwood et al. (Ann. Geophys., 2014) and analysed using the OSF continuity model of Solanki at al. (Nature, 2000) which employs a constant fractional OSF loss rate; iii) the same OSF data analysed using the OSF continuity model of Owens and Lockwood (J.G.R., 2012) in which the fractional loss rate varies with the tilt of the heliospheric current sheet and hence with the phase of the solar cycle; iv) the occurrence frequency of low-latitude aurora for 1780-1980 from the survey of Legrand and Simon (Ann. Geophys., 1987). For all cases, $R_{BB}$ exceeds the test terrestrial series by an amount that increases as one goes back in time.
-
tests of Sunspot Number sequences 1 using ionosonde data
Solar Physics, 2016Co-Authors: Mike Lockwood, M J Owens, Luke Barnard, Chris J Scott, D M WillisAbstract:More than 70 years ago, it was recognised that ionospheric F2-layer critical frequencies [foF2] had a strong relationship to Sunspot Number. Using historic datasets from the Slough and Washington ionosondes, we evaluate the best statistical fits of foF2 to Sunspot Numbers (at each Universal Time [UT] separately) in order to search for drifts and abrupt changes in the fit residuals over Solar Cycles 17 – 21. This test is carried out for the original composite of the Wolf/Zurich/International Sunspot Number [ $R$ ], the new “backbone” group Sunspot Number [ $R_{\mathrm{BB}}$ ], and the proposed “corrected Sunspot Number” [ $R_{\mathrm{C}}$ ]. Polynomial fits are made both with and without allowance for the white-light facular area, which has been reported as being associated with cycle-to-cycle changes in the Sunspot-Number–foF2 relationship. Over the interval studied here, $R$ , $R_{\mathrm{BB}}$ , and $R_{\mathrm{C}}$ largely differ in their allowance for the “Waldmeier discontinuity” around 1945 (the correction factor for which for $R$ , $R_{\mathrm{BB}}$ , and $R_{\mathrm{C}}$ is, respectively, zero, effectively over 20 %, and explicitly 11.6 %). It is shown that for Solar Cycles 18 – 21, all three Sunspot data sequences perform well, but that the fit residuals are lowest and most uniform for $R_{\mathrm{BB}}$ . We here use foF2 for those UTs for which $R$ , $R_{\mathrm{BB}}$ , and $R_{\mathrm{C}}$ all give correlations exceeding 0.99 for intervals both before and after the Waldmeier discontinuity. The error introduced by the Waldmeier discontinuity causes $R$ to underestimate the fitted values based on the foF2 data for 1932 – 1945, but $R_{\mathrm{BB}}$ overestimates them by almost the same factor, implying that the correction for the Waldmeier discontinuity inherent in $R_{\mathrm{BB}}$ is too large by a factor of two. Fit residuals are smallest and most uniform for $R_{\mathrm{C}}$ , and the ionospheric data support the optimum discontinuity multiplicative correction factor derived from the independent Royal Greenwich Observatory (RGO) Sunspot group data for the same interval.
Mike Lockwood - One of the best experts on this subject based on the ideXlab platform.
-
tests of Sunspot Number sequences 4 discontinuities around 1946 in various Sunspot Number and Sunspot group Number reconstructions
Solar Physics, 2016Co-Authors: Mike Lockwood, M J Owens, Luke BarnardAbstract:We use five test data series to search for, and quantify, putative discontinuities around 1946 in five different annual-mean Sunspot-Number or Sunspot-group-Number data sequences. The data series tested are the original and new versions of the Wolf/Zurich/International Sunspot Number composite [ $R_{\text{ISNv1}}$ and $R_{\text{ISNv2}}$ ] (respectively Clette et al. in Adv. Space Res. 40, 919, 2007 and Clette et al. in The Solar Activity Cycle 35, Springer, New York, 2015); the corrected version of $R$ ISNv1 proposed by Lockwood, Owens, and Barnard (J. Geophys. Res. 119, 5193, 2014a) [ $R _{\mathrm{C}}$ ]; the new “backbone” group-Number composite proposed by Svalgaard and Schatten (Solar Phys. 291, 2016) [ $R_{\text{BB}}$ ]; and the new group-Number composite derived by Usoskin et al. (Solar Phys. 291, 2016) [ $R_{\text{UEA}}$ ]. The test data series used are the group-Number [ $N_{\mathrm{G}}$ ] and total Sunspot area [ $A _{\mathrm{G}}$ ] from the Royal Observatory, Greenwich/Royal Greenwich Observatory (RGO) photoheliographic data; the Ca K index from the recent re-analysis of Mount Wilson Observatory (MWO) spectroheliograms in the Calcium ii K ion line; the Sunspot-group-Number from the MWO Sunspot drawings [ $N_{\text{MWO}}$ ]; and the dayside ionospheric F2-region critical frequencies measured by the Slough ionosonde [foF2]. These test data all vary in close association with Sunspot Numbers, in some cases non-linearly. The tests are carried out using both the before-and-after fit-residual comparison method and the correlation method of Lockwood, Owens, and Barnard, applied to annual mean data for intervals iterated to minimise errors and to eliminate uncertainties associated with the precise date of the putative discontinuity. It is not assumed that the correction required is by a constant factor, nor even linear in Sunspot Number. It is shown that a non-linear correction is required by $R_{\mathrm{C}}$ , $R_{\mathrm{BB}}$ , and $R_{\text{ISNv1}}$ , but not by $R_{\text{ISNv2}}$ or $R_{\text{UEA}}$ . The five test datasets give very similar results in all cases. By multiplying the probability distribution functions together, we obtain the optimum correction for each Sunspot dataset that must be applied to pre-discontinuity data to make them consistent with the post-discontinuity data. It is shown that, on average, values for 1932 – 1943 are too low (relative to later values) by about 12.3 % for $R_{\text{ISNv1}}$ but are too high for $R_{\text{ISNv2}}$ and $R_{\mathrm{BB}}$ by 3.8 % and 5.2 %, respectively. The correction that was applied to generate $R_{\mathrm{C}}$ from $R$ ISNv1 reduces this average factor to 0.5 % but does not remove the non-linear variation with the test data, and other errors remain uncorrected. A valuable test of the procedures used is provided by $R_{\text{UEA}}$ , which is identical to the RGO $N_{\mathrm{G}}$ values over the interval employed.
-
tests of Sunspot Number sequences 2 using geomagnetic and auroral data
Solar Physics, 2016Co-Authors: Mike Lockwood, M J Owens, Luke Barnard, Chris J Scott, Heikki NevanlinnaAbstract:We compare four Sunspot-Number data sequences against geomagnetic and terrestrial auroral observations. The comparisons are made for the original Solar Influences Data Center (SIDC) composite of Wolf/Zurich/International Sunspot Number [ $R_{\text{ISNv}1}$ ], the group Sunspot Number [ $R_{\mathrm{G}}$ ] by Hoyt and Schatten (Solar Phys. 181, 491, 1998), the new “backbone” group Sunspot Number [ $R_{\mathrm{BB}}$ ] by Svalgaard and Schatten (Solar Phys., , 2016), and the “corrected” Sunspot Number [ $R_{\mathrm{C}}$ ] by Lockwood, Owens, and Barnard (J. Geophys. Res. 119, 5172, 2014a). Each Sunspot Number is fitted with terrestrial observations, or parameters derived from terrestrial observations to be linearly proportional to Sunspot Number, over a 30-year calibration interval of 1982 – 2012. The fits are then used to compute test sequences, which extend further back in time and which are compared to $R_{\text{ISNv}1}$ , $R_{\mathrm{G}}$ , $R_{\text{BB}}$ , and $R_{\mathrm{C}}$ . To study the long-term trends, comparisons are made using averages over whole solar cycles (minimum-to-minimum). The test variations are generated in four ways: i) using the IDV(1d) and IDV geomagnetic indices (for 1845 – 2013) fitted over the calibration interval using the various Sunspot Numbers and the phase of the solar cycle; ii) from the open solar flux (OSF) generated for 1845 – 2013 from four pairings of geomagnetic indices by Lockwood et al. (Ann. Geophys. 32, 383, 2014a) and analysed using the OSF continuity model of Solanki, Schussler, and Fligge (Nature, 408, 445, 2000), which employs a constant fractional OSF loss rate; iii) the same OSF data analysed using the OSF continuity model of Owens and Lockwood (J. Geophys. Res. 117, A04102, 2012), in which the fractional loss rate varies with the tilt of the heliospheric current sheet and hence with the phase of the solar cycle; iv) the occurrence frequency of low-latitude aurora for 1780 – 1980 from the survey of Legrand and Simon (Ann. Geophys. 5, 161, 1987). For all cases, $R_{\mathrm{BB}}$ exceeds the test terrestrial series by an amount that increases as one goes back in time.
-
tests of Sunspot Number sequences 4 discontinuities around 1946 in various Sunspot Number and Sunspot group Number reconstructions
arXiv: Solar and Stellar Astrophysics, 2016Co-Authors: Mike Lockwood, M J Owens, Luke BarnardAbstract:We use 5 test data series to quantify putative discontinuities around 1946 in 5 annual-mean Sunspot Number or group Number sequences. The series tested are: the original and new versions of the Wolf/Zurich/International Sunspot Number composite [$R_{ISNv1}$ and $R_{ISNv2}$] ; the corrected version of $R_{ISNv1}$ [$R_C$]; the backbone group Number [$R_{BB}$]; and the group Number composite [$R_{UEA}$]. The test data are: the group Number $N_G$ and total Sunspot area $A_G$ from the RGO photoheliographic data; the CaK index from re-analysis of MWO CaII K spectroheliograms; the group Number from the MWO Sunspot drawings, $N_{MWO}$; and ionospheric critical frequencies at Slough [$foF2$]. The test data all vary with Sunspot Numbers, in some cases non-linearly. Tests use both before-and-after fit-residual comparison and correlation methods, applied to intervals iterated to minimise errors and eliminate the effect of the discontinuity date. It is not assumed that the correction required is by a constant factor, nor even linear in Sunspot Number. A non-linear correction is required by $R_C$, $R_{BB}$ and $R_{ISNv1}$, but not by $R_{ISNv2}$ or $R_{UEA}$. The test datasets give very similar results in all cases. By multiplying the probability distribution functions together we obtain the optimum correction for each data series that must be applied to pre-discontinuity data to make them consistent with the post-discontinuity data. It is shown that, on average, values for 1932-1943 are too small (relative to later values) by about 12.3% for $R_{ISNv1}$ but are too large for $R_{ISNv2}$ and $R_{BB}$ by 3.8% and 5.2%. The correction applied to generate $R_C$ from $R_{ISNv1}$ reduces this average factor to 0.5% but does not remove the non-linear variation, and other errors remain uncorrected. A test is provided by $R_{UEA}$, which is identical to the RGO $N_G$ values over the interval used.
-
tests of Sunspot Number sequences 2 using geomagnetic and auroral data
arXiv: Solar and Stellar Astrophysics, 2016Co-Authors: Mike Lockwood, M J Owens, Luke Barnard, Chris J Scott, Heikki NevanlinnaAbstract:We compare four Sunspot-Number data sequences against geomagnetic and terrestrial auroral observations. The comparisons are made for the original SIDC composite of Wolf-Zurich-International Sunspot Number [$R_{ISNv1}$], the group Sunspot Number [$R_{G}$] by Hoyt and Schatten (Solar Phys., 1998), the new "backbone" group Sunspot Number [$R_{BB}$] by Svalgaard and Schatten (Solar Phys., 2016), and the "corrected" Sunspot Number [$R_{C}$] by Lockwood at al. (J.G.R., 2014). Each Sunspot Number is fitted with terrestrial observations, or parameters derived from terrestrial observations to be linearly proportional to Sunspot Number, over a 30-year calibration interval of 1982-2012. The fits are then used to compute test sequences, which extend further back in time and which are compared to $R_{ISNv1}$, $R_{G}$, $R_{BB}$, and $R_{C}$. To study the long-term trends, comparisons are made using averages over whole solar cycles (minimum-to-minimum). The test variations are generated in four ways: i) using the IDV(1d) and IDV geomagnetic indices (for 1845-2013) fitted over the calibration interval using the various Sunspot Numbers and the phase of the solar cycle; ii) from the open solar flux (OSF) generated for 1845 - 2013 from four pairings of geomagnetic indices by Lockwood et al. (Ann. Geophys., 2014) and analysed using the OSF continuity model of Solanki at al. (Nature, 2000) which employs a constant fractional OSF loss rate; iii) the same OSF data analysed using the OSF continuity model of Owens and Lockwood (J.G.R., 2012) in which the fractional loss rate varies with the tilt of the heliospheric current sheet and hence with the phase of the solar cycle; iv) the occurrence frequency of low-latitude aurora for 1780-1980 from the survey of Legrand and Simon (Ann. Geophys., 1987). For all cases, $R_{BB}$ exceeds the test terrestrial series by an amount that increases as one goes back in time.
-
tests of Sunspot Number sequences 1 using ionosonde data
Solar Physics, 2016Co-Authors: Mike Lockwood, M J Owens, Luke Barnard, Chris J Scott, D M WillisAbstract:More than 70 years ago, it was recognised that ionospheric F2-layer critical frequencies [foF2] had a strong relationship to Sunspot Number. Using historic datasets from the Slough and Washington ionosondes, we evaluate the best statistical fits of foF2 to Sunspot Numbers (at each Universal Time [UT] separately) in order to search for drifts and abrupt changes in the fit residuals over Solar Cycles 17 – 21. This test is carried out for the original composite of the Wolf/Zurich/International Sunspot Number [ $R$ ], the new “backbone” group Sunspot Number [ $R_{\mathrm{BB}}$ ], and the proposed “corrected Sunspot Number” [ $R_{\mathrm{C}}$ ]. Polynomial fits are made both with and without allowance for the white-light facular area, which has been reported as being associated with cycle-to-cycle changes in the Sunspot-Number–foF2 relationship. Over the interval studied here, $R$ , $R_{\mathrm{BB}}$ , and $R_{\mathrm{C}}$ largely differ in their allowance for the “Waldmeier discontinuity” around 1945 (the correction factor for which for $R$ , $R_{\mathrm{BB}}$ , and $R_{\mathrm{C}}$ is, respectively, zero, effectively over 20 %, and explicitly 11.6 %). It is shown that for Solar Cycles 18 – 21, all three Sunspot data sequences perform well, but that the fit residuals are lowest and most uniform for $R_{\mathrm{BB}}$ . We here use foF2 for those UTs for which $R$ , $R_{\mathrm{BB}}$ , and $R_{\mathrm{C}}$ all give correlations exceeding 0.99 for intervals both before and after the Waldmeier discontinuity. The error introduced by the Waldmeier discontinuity causes $R$ to underestimate the fitted values based on the foF2 data for 1932 – 1945, but $R_{\mathrm{BB}}$ overestimates them by almost the same factor, implying that the correction for the Waldmeier discontinuity inherent in $R_{\mathrm{BB}}$ is too large by a factor of two. Fit residuals are smallest and most uniform for $R_{\mathrm{C}}$ , and the ionospheric data support the optimum discontinuity multiplicative correction factor derived from the independent Royal Greenwich Observatory (RGO) Sunspot group data for the same interval.
M J Owens - One of the best experts on this subject based on the ideXlab platform.
-
assessment of different Sunspot Number series using the cosmogenic isotope 44 ti in meteorites
Monthly Notices of the Royal Astronomical Society, 2017Co-Authors: Eleanna Asvestari, M J Owens, Gennady A Kovaltsov, N A Krivova, Sara Rubinetti, C TariccoAbstract:Many Sunspot Number series exist suggesting different levels of solar activity during the past centuries. Their reliability can be assessed only by comparing them with alternative indirect proxies. We test different Sunspot Number series against the updated record of cosmogenic radionuclide 44Ti measured in meteorites. Two bounding scenarios of solar activity changes have been considered: the HH-scenario (based on the series by Svalgaard and Schatten), in particular, predicting moderate activity during the Maunder minimum, and the LL-scenario (based on the RG series by Lockwood et al.) predicting moderate activity for the 18th–19th centuries and the very low activity level for the Maunder minimum. For each scenario, the magnetic open solar flux, the heliospheric modulation potential and the expected production of 44Ti were computed. The calculated production rates were compared with the corresponding measurements of 44Ti activity in stony meteorites fallen since 1766. The analysis reveals that the LL-scenario is fully consistent with the measured 44Ti data, in particular, recovering the observed secular trend between the 17th century and the Modern grand maximum. On the contrary, the HH-scenario appears significantly inconsistent with the data, mostly due to the moderate level of activity during the Maunder minimum. It is concluded that the HH-scenario Sunspot Number reconstruction significantly overestimates solar activity prior to the mid-18th century, especially during the Maunder minimum. The exact level of solar activity after 1750 cannot be distinguished with this method, since both H- and L- scenarios appear statistically consistent with the data.
-
tests of Sunspot Number sequences 4 discontinuities around 1946 in various Sunspot Number and Sunspot group Number reconstructions
Solar Physics, 2016Co-Authors: Mike Lockwood, M J Owens, Luke BarnardAbstract:We use five test data series to search for, and quantify, putative discontinuities around 1946 in five different annual-mean Sunspot-Number or Sunspot-group-Number data sequences. The data series tested are the original and new versions of the Wolf/Zurich/International Sunspot Number composite [ $R_{\text{ISNv1}}$ and $R_{\text{ISNv2}}$ ] (respectively Clette et al. in Adv. Space Res. 40, 919, 2007 and Clette et al. in The Solar Activity Cycle 35, Springer, New York, 2015); the corrected version of $R$ ISNv1 proposed by Lockwood, Owens, and Barnard (J. Geophys. Res. 119, 5193, 2014a) [ $R _{\mathrm{C}}$ ]; the new “backbone” group-Number composite proposed by Svalgaard and Schatten (Solar Phys. 291, 2016) [ $R_{\text{BB}}$ ]; and the new group-Number composite derived by Usoskin et al. (Solar Phys. 291, 2016) [ $R_{\text{UEA}}$ ]. The test data series used are the group-Number [ $N_{\mathrm{G}}$ ] and total Sunspot area [ $A _{\mathrm{G}}$ ] from the Royal Observatory, Greenwich/Royal Greenwich Observatory (RGO) photoheliographic data; the Ca K index from the recent re-analysis of Mount Wilson Observatory (MWO) spectroheliograms in the Calcium ii K ion line; the Sunspot-group-Number from the MWO Sunspot drawings [ $N_{\text{MWO}}$ ]; and the dayside ionospheric F2-region critical frequencies measured by the Slough ionosonde [foF2]. These test data all vary in close association with Sunspot Numbers, in some cases non-linearly. The tests are carried out using both the before-and-after fit-residual comparison method and the correlation method of Lockwood, Owens, and Barnard, applied to annual mean data for intervals iterated to minimise errors and to eliminate uncertainties associated with the precise date of the putative discontinuity. It is not assumed that the correction required is by a constant factor, nor even linear in Sunspot Number. It is shown that a non-linear correction is required by $R_{\mathrm{C}}$ , $R_{\mathrm{BB}}$ , and $R_{\text{ISNv1}}$ , but not by $R_{\text{ISNv2}}$ or $R_{\text{UEA}}$ . The five test datasets give very similar results in all cases. By multiplying the probability distribution functions together, we obtain the optimum correction for each Sunspot dataset that must be applied to pre-discontinuity data to make them consistent with the post-discontinuity data. It is shown that, on average, values for 1932 – 1943 are too low (relative to later values) by about 12.3 % for $R_{\text{ISNv1}}$ but are too high for $R_{\text{ISNv2}}$ and $R_{\mathrm{BB}}$ by 3.8 % and 5.2 %, respectively. The correction that was applied to generate $R_{\mathrm{C}}$ from $R$ ISNv1 reduces this average factor to 0.5 % but does not remove the non-linear variation with the test data, and other errors remain uncorrected. A valuable test of the procedures used is provided by $R_{\text{UEA}}$ , which is identical to the RGO $N_{\mathrm{G}}$ values over the interval employed.
-
tests of Sunspot Number sequences 2 using geomagnetic and auroral data
Solar Physics, 2016Co-Authors: Mike Lockwood, M J Owens, Luke Barnard, Chris J Scott, Heikki NevanlinnaAbstract:We compare four Sunspot-Number data sequences against geomagnetic and terrestrial auroral observations. The comparisons are made for the original Solar Influences Data Center (SIDC) composite of Wolf/Zurich/International Sunspot Number [ $R_{\text{ISNv}1}$ ], the group Sunspot Number [ $R_{\mathrm{G}}$ ] by Hoyt and Schatten (Solar Phys. 181, 491, 1998), the new “backbone” group Sunspot Number [ $R_{\mathrm{BB}}$ ] by Svalgaard and Schatten (Solar Phys., , 2016), and the “corrected” Sunspot Number [ $R_{\mathrm{C}}$ ] by Lockwood, Owens, and Barnard (J. Geophys. Res. 119, 5172, 2014a). Each Sunspot Number is fitted with terrestrial observations, or parameters derived from terrestrial observations to be linearly proportional to Sunspot Number, over a 30-year calibration interval of 1982 – 2012. The fits are then used to compute test sequences, which extend further back in time and which are compared to $R_{\text{ISNv}1}$ , $R_{\mathrm{G}}$ , $R_{\text{BB}}$ , and $R_{\mathrm{C}}$ . To study the long-term trends, comparisons are made using averages over whole solar cycles (minimum-to-minimum). The test variations are generated in four ways: i) using the IDV(1d) and IDV geomagnetic indices (for 1845 – 2013) fitted over the calibration interval using the various Sunspot Numbers and the phase of the solar cycle; ii) from the open solar flux (OSF) generated for 1845 – 2013 from four pairings of geomagnetic indices by Lockwood et al. (Ann. Geophys. 32, 383, 2014a) and analysed using the OSF continuity model of Solanki, Schussler, and Fligge (Nature, 408, 445, 2000), which employs a constant fractional OSF loss rate; iii) the same OSF data analysed using the OSF continuity model of Owens and Lockwood (J. Geophys. Res. 117, A04102, 2012), in which the fractional loss rate varies with the tilt of the heliospheric current sheet and hence with the phase of the solar cycle; iv) the occurrence frequency of low-latitude aurora for 1780 – 1980 from the survey of Legrand and Simon (Ann. Geophys. 5, 161, 1987). For all cases, $R_{\mathrm{BB}}$ exceeds the test terrestrial series by an amount that increases as one goes back in time.
-
tests of Sunspot Number sequences 4 discontinuities around 1946 in various Sunspot Number and Sunspot group Number reconstructions
arXiv: Solar and Stellar Astrophysics, 2016Co-Authors: Mike Lockwood, M J Owens, Luke BarnardAbstract:We use 5 test data series to quantify putative discontinuities around 1946 in 5 annual-mean Sunspot Number or group Number sequences. The series tested are: the original and new versions of the Wolf/Zurich/International Sunspot Number composite [$R_{ISNv1}$ and $R_{ISNv2}$] ; the corrected version of $R_{ISNv1}$ [$R_C$]; the backbone group Number [$R_{BB}$]; and the group Number composite [$R_{UEA}$]. The test data are: the group Number $N_G$ and total Sunspot area $A_G$ from the RGO photoheliographic data; the CaK index from re-analysis of MWO CaII K spectroheliograms; the group Number from the MWO Sunspot drawings, $N_{MWO}$; and ionospheric critical frequencies at Slough [$foF2$]. The test data all vary with Sunspot Numbers, in some cases non-linearly. Tests use both before-and-after fit-residual comparison and correlation methods, applied to intervals iterated to minimise errors and eliminate the effect of the discontinuity date. It is not assumed that the correction required is by a constant factor, nor even linear in Sunspot Number. A non-linear correction is required by $R_C$, $R_{BB}$ and $R_{ISNv1}$, but not by $R_{ISNv2}$ or $R_{UEA}$. The test datasets give very similar results in all cases. By multiplying the probability distribution functions together we obtain the optimum correction for each data series that must be applied to pre-discontinuity data to make them consistent with the post-discontinuity data. It is shown that, on average, values for 1932-1943 are too small (relative to later values) by about 12.3% for $R_{ISNv1}$ but are too large for $R_{ISNv2}$ and $R_{BB}$ by 3.8% and 5.2%. The correction applied to generate $R_C$ from $R_{ISNv1}$ reduces this average factor to 0.5% but does not remove the non-linear variation, and other errors remain uncorrected. A test is provided by $R_{UEA}$, which is identical to the RGO $N_G$ values over the interval used.
-
tests of Sunspot Number sequences 2 using geomagnetic and auroral data
arXiv: Solar and Stellar Astrophysics, 2016Co-Authors: Mike Lockwood, M J Owens, Luke Barnard, Chris J Scott, Heikki NevanlinnaAbstract:We compare four Sunspot-Number data sequences against geomagnetic and terrestrial auroral observations. The comparisons are made for the original SIDC composite of Wolf-Zurich-International Sunspot Number [$R_{ISNv1}$], the group Sunspot Number [$R_{G}$] by Hoyt and Schatten (Solar Phys., 1998), the new "backbone" group Sunspot Number [$R_{BB}$] by Svalgaard and Schatten (Solar Phys., 2016), and the "corrected" Sunspot Number [$R_{C}$] by Lockwood at al. (J.G.R., 2014). Each Sunspot Number is fitted with terrestrial observations, or parameters derived from terrestrial observations to be linearly proportional to Sunspot Number, over a 30-year calibration interval of 1982-2012. The fits are then used to compute test sequences, which extend further back in time and which are compared to $R_{ISNv1}$, $R_{G}$, $R_{BB}$, and $R_{C}$. To study the long-term trends, comparisons are made using averages over whole solar cycles (minimum-to-minimum). The test variations are generated in four ways: i) using the IDV(1d) and IDV geomagnetic indices (for 1845-2013) fitted over the calibration interval using the various Sunspot Numbers and the phase of the solar cycle; ii) from the open solar flux (OSF) generated for 1845 - 2013 from four pairings of geomagnetic indices by Lockwood et al. (Ann. Geophys., 2014) and analysed using the OSF continuity model of Solanki at al. (Nature, 2000) which employs a constant fractional OSF loss rate; iii) the same OSF data analysed using the OSF continuity model of Owens and Lockwood (J.G.R., 2012) in which the fractional loss rate varies with the tilt of the heliospheric current sheet and hence with the phase of the solar cycle; iv) the occurrence frequency of low-latitude aurora for 1780-1980 from the survey of Legrand and Simon (Ann. Geophys., 1987). For all cases, $R_{BB}$ exceeds the test terrestrial series by an amount that increases as one goes back in time.
J M Vaquero - One of the best experts on this subject based on the ideXlab platform.
-
visualization of the challenges and limitations of the long term Sunspot Number record
Nature Astronomy, 2019Co-Authors: Andres Munozjaramillo, J M VaqueroAbstract:The solar cycle periodically reshapes the magnetic structure and radiative output of the Sun and determines its impact on the heliosphere roughly every 11 years. Besides this main periodicity, it shows century-long variations (including periods of abnormally low solar activity called grand minima). The Maunder Minimum (1645–1715) has generated significant interest as the archetype of a grand minimum in magnetic activity for the Sun and other stars, suggesting a potential link between the Sun and changes in terrestrial climate. Recent reanalyses of Sunspot observations have yielded a conflicted view on the evolution of solar activity during the past 400 years (a steady increase versus a constant level). This has ignited a concerted community-wide effort to understand the depth of the Maunder Minimum and the subsequent secular evolution of solar activity. The goal of this Perspective is to review recent work that uses historical data to estimate long-term solar variability, and to provide context to users of these estimates that may not be aware of their limitations. We propose a clear visual guide than can be used to easily assess observational coverage for different periods, as well as the level of disagreement between currently proposed Sunspot group Number series. The Sunspot Number time series is an essential tool to determine the secular variations of solar activity, but particular care must be taken to handle and present incomplete temporal coverage. The authors present the current state of research and propose a new way to visualize long-term solar activity data.
-
extreme value theory applied to the millennial Sunspot Number series
arXiv: Solar and Stellar Astrophysics, 2018Co-Authors: F J Acero, M C Gallego, Jose Alvarez Garcia, J M VaqueroAbstract:In this work, we use two decadal Sunspot Number series reconstructed from cosmogenic radionuclide data (14C in tree trunks, SN-14C and 10Be in polar ice, SN-10Be) and the Extreme Value Theory to study variability of solar activity during the last 9 millennia. The peaks-over-threshold technique was used to compute, in particular, the shape parameter of the generalized Pareto distribution for different thresholds. Its negative value implies an upper bound of the extreme SN-10Be and SN-14C time series. The return level for 1000 and 10000 years were estimated leading to values lower than the maximum observed values, expected for the 1000-year, but not for the 10000-year return levels, for both series. A comparison of these results with those obtained using the observed Sunspot Numbers from telescopic observations during the last four centuries suggest that the main characteristics of solar activity have already been recorded in the telescopic period (from 1610 to nowadays) which covers the full range of solar variability from a Grand minimum to a Grand maximum.
-
extreme value theory applied to the millennial Sunspot Number series
The Astrophysical Journal, 2018Co-Authors: F J Acero, M C Gallego, Jose Alvarez Garcia, J M VaqueroAbstract:In this work, we use two decadal Sunspot Number series reconstructed from cosmogenic radionuclide data (14C in tree trunks, SN 14C, and 10Be in polar ice, SN 10Be) and the extreme value theory to study variability of solar activity during the last nine millennia. The peaks-over-threshold technique was used to compute, in particular, the shape parameter of the generalized Pareto distribution for different thresholds. Its negative value implies an upper bound of the extreme SN 10Be and SN 14C timeseries. The return level for 1000 and 10,000 years were estimated leading to values lower than the maximum observed values, expected for the 1000 year, but not for the 10,000 year return levels, for both series. A comparison of these results with those obtained using the observed Sunspot Numbers from telescopic observations during the last four centuries suggests that the main characteristics of solar activity have already been recorded in the telescopic period (from 1610 to nowadays) which covers the full range of solar variability from a Grand minimum to a Grand maximum.
-
analysing spotless days as predictors of solar activity from the new Sunspot Number
Solar Physics, 2017Co-Authors: V M S Carrasco, J M Vaquero, M C GallegoAbstract:The use of spotless days to predict future solar activity is revised here based on the new version of the Sunspot Number index with a 24-month filter. Data from Solar Cycle (SC) 10 are considered because the temporal coverage of the records is 100% for this solar cycle. The interrelationships of the timing characteristics of spotless days and their comparison with Sunspot cycle parameters are explored; in some cases, we find very strong correlations. Such is the case for the relationship between the minimum time between spotless days either side of a given solar maximum and the maximum time between spotless days either side of the previous solar minimum, with $r = -0.91$ and a $p\mbox{-value} < 0.001$ . However, the predictions for SCs 24 or 23 made by other authors in previous works using spotless days as a predictor of solar activity are not correct since the predictions have not been fulfilled. Although there seems to be a pattern of strong correlation for some relationships between the parameters that have been studied, a prediction of future solar cycles from these parameters defined as functions of spotless days should be made with caution because the estimated values are sometimes far from the observed ones. Furthermore, SC 23 seems to show a mode change, a break with respect to the behaviour of previous solar cycles and more similar to SCs 10 – 15.
-
analysing the spotless days as predictors of the solar activity from the new Sunspot Number
arXiv: Solar and Stellar Astrophysics, 2017Co-Authors: V M S Carrasco, J M Vaquero, M C GallegoAbstract:The use of the spotless days to predict the future solar activity is here revised based on the new version of the Sunspot Number index with a 24-month filter. Data from Solar Cycle (SC) 10 are considered because from this solar cycle the temporal coverage of the records is 100 %. The interrelationships of the timing characteristics of spotless days and their comparison with Sunspot cycle parameters are explored, in some cases finding very strong correlations. Such is the case for the relationship between the minimum time between spotless days either side of a given solar maximum and the maximum time between spotless days either side in the previous solar minimum, with r = -0.91 and a p-value < 0.001. However, the predictions for SC 24 or 23 made by other authors in previous works using the spotless days as a predictor of solar activity are not good since it has not been fulfilled. Although there seems to be a pattern of strong correlation for some relationships between the parameters studied, prediction of future solar cycles from these parameters defined as functions of the spotless days should be made with caution because sometimes the estimated values are far from the observed ones. Finally, SC 23 seems to show a mode change, a break respect to the behavior of their previous solar cycles and more similar to SC 10-15.
E W Cliver - One of the best experts on this subject based on the ideXlab platform.
-
evolution of the Sunspot Number and solar wind time series
Space Science Reviews, 2018Co-Authors: E W Cliver, Konstantin HerbstAbstract:The past two decades have witnessed significant changes in our knowledge of long-term solar and solar wind activity. The Sunspot Number time series (1700-present) developed by Rudolf Wolf during the second half of the 19th century was revised and extended by the group Sunspot Number series (1610–1995) of Hoyt and Schatten during the 1990s. The group Sunspot Number is significantly lower than the Wolf series before ∼1885. An effort from 2011–2015 to understand and remove differences between these two series via a series of workshops had the unintended consequence of prompting several alternative constructions of the Sunspot Number. Thus it has been necessary to expand and extend the Sunspot Number reconciliation process. On the solar wind side, after a decade of controversy, an ISSI International Team used geomagnetic and Sunspot data to obtain a high-confidence time series of the solar wind magnetic field strength ( $B$ ) from 1750-present that can be compared with two independent long-term (> ∼600 year) series of annual $B$ -values based on cosmogenic nuclides. In this paper, we trace the twists and turns leading to our current understanding of long-term solar and solar wind activity.
-
Preface to Topical Issue: Recalibration of the Sunspot Number
Solar Physics, 2016Co-Authors: Frederic Clette, Leif Svalgaard, J M Vaquero, E W Cliver, L. Lefèvre, J. W. LeibacherAbstract:This topical issue contains articles on the effort to recalibrate the Sunspot Number (SN) that was initiated by the Sunspot Number Workshops. These workshops led to a revision of the Wolf Sunspot Number (WSN) and a new construction of the group Sunspot Number (GSN), both published herein. In addition, this topical issue includes three independently proposed alternative SN time series (two Wolf and one group), as well as articles providing historical context, critical assessments, correlative analyses, and observational data, both historical and modern, pertaining to the Sunspot-Number time series. The ongoing effort to understand and reconcile the differences between the various new Sunspot Number series is briefly discussed.
-
comparison of new and old Sunspot Number time series
Solar Physics, 2016Co-Authors: E W CliverAbstract:Four new Sunspot Number time series have been published in this Topical Issue: a backbone-based group Number in Svalgaard and Schatten (Solar Phys., 2016; referred to here as $\mathit{SS}$ , 1610 – present), a group Number series in Usoskin et al. (Solar Phys., 2016; UEA, 1749 – present) that employs active day fractions from which it derives an observational threshold in group spot area as a measure of observer merit, a provisional group Number series in Cliver and Ling (Solar Phys., 2016; $\mathit{CL}$ , 1841 – 1976) that removed flaws in the Hoyt and Schatten (Solar Phys. 179, 189, 1998a; 181, 491, 1998b) normalization scheme for the original relative group Sunspot Number ( $R_{\mathrm{G}}$ , 1610 – 1995), and a corrected Wolf (international, $R_{\mathrm{I}}$ ) Number in Clette and Lefevre (Solar Phys., 2016; $S_{\mathrm{N}}$ , 1700 – present). Despite quite different construction methods, the four new series agree well after about 1900. Before 1900, however, the UEA time series is lower than $\mathit{SS}$ , $\mathit{CL}$ , and $S_{\mathrm{N}}$ , particularly so before about 1885. Overall, the UEA series most closely resembles the original $R_{\mathrm{G}}$ series. Comparison of the UEA and SS series with a new solar wind $B$ time series (Owens et al. in J. Geophys. Res., 2016; 1845 – present) indicates that the UEA time series is too low before 1900. We point out incongruities in the Usoskin et al. (Solar Phys., 2016) observer normalization scheme and present evidence that this method under-estimates group counts before 1900. In general, a correction factor time series, obtained by dividing an annual group count series by the corresponding yearly averages of raw group counts for all observers, can be used to assess the reliability of new Sunspot Number reconstructions.
-
the discontinuity circa 1885 in the group Sunspot Number
Solar Physics, 2016Co-Authors: E W Cliver, A G LingAbstract:On average, the international Sunspot Number ( $R_{\mathrm{I}}$ ) is 44 % higher than the group Sunspot Number ( $R_{\mathrm{G}}$ ) from 1885 to the beginning of the $R_{\mathrm{I}}$ series in 1700. This is the principal difference between $R_{\mathrm{I}}$ and $R_{\mathrm{G}}$ . Here we show that this difference is primarily due to an inhomogeneity in the Royal Greenwich Observatory (RGO) record of Sunspot groups (1874 – 1976) used to derive observer normalization factors (called $k$ -factors) for $R_{\mathrm{G}}$ . Specifically, annual RGO group counts increase relative to those of Wolfer and other long-term observers from 1876 – 1915. A secondary contributing cause is that the $k$ -factors for observers who began observing before 1884 and overlapped with RGO for any years during 1874 – 1883 were not based on direct comparison with RGO but were calculated using one or more intermediary or additional observers. We introduce $R_{\mathrm{GC}}$ by rectifying the RGO group counts from 1874 – 1915 and basing $k$ -factors on direct comparison with RGO across the 1885 discontinuity, which brings the $R_{\mathrm{G}}$ and $R_{\mathrm{I}}$ series into reasonable agreement for the 1841 – 1885 interval (after correcting $R_{\mathrm{I}}$ for an inhomogeneity from 1849 – 1867 (to give $R_{\mathrm{IC}}$ )). Comparison with an independently derived backbone-based reconstruction of $R_{\mathrm{G}}$ ( $R_{\mathrm{BB}}$ ) indicates that $R_{\mathrm{GC}}$ over-corrects $R_{\mathrm{BB}}$ by 4 % on average from 1841 – 1925. Our analysis suggests that the maxima of Cycles 10 (in 1860), 12 (1883/1884), and 13 (1893) in the $R_{\mathrm{IC}}$ series are too low by ≈ 10 %.
-
revisiting the Sunspot Number a 400 year perspective on the solar cycle
Space Science Reviews, 2014Co-Authors: Frederic Clette, Leif Svalgaard, J M Vaquero, E W CliverAbstract:Our knowledge of the long-term evolution of solar activity and of its primary modulation, the 11-year cycle, largely depends on a single direct observational record: the visual Sunspot counts that retrace the last 4 centuries, since the invention of the astronomical telescope. Currently, this activity index is available in two main forms: the International Sunspot Number initiated by R. Wolf in 1849 and the Group Number constructed more recently by Hoyt and Schatten (Sol. Phys. 179:189–219, 1998a, 181:491–512, 1998b). Unfortunately, those two series do not match by various aspects, inducing confusions and contradictions when used in crucial contemporary studies of the solar dynamo or of the solar forcing on the Earth climate. Recently, new efforts have been undertaken to diagnose and correct flaws and biases affecting both Sunspot series, in the framework of a series of dedicated Sunspot Number Workshops. Here, we present a global overview of our current understanding of the Sunspot Number calibration.
