The interplanetary magnetic field (IMF) is the magnetic field of the Sun stretched out by the solar wind. The polarity of the IMF is either positive or negative according to the polarity of the original solar magnetic field. The equivalent ionospheric Disturbance Polar current powered by the azimuthal Y component current system is located at polar latitudes and provides specific geomagnetic variations. It is known that the configuration of this system depends on the polarity of the IMF. Thus, in the absence of direct data in the presatellite era, the IMF sector structure could only be inferred from ground-based geomagnetic observations (Svalgaard,1968; Mansurov,1969). In this paper the IMF polarities have been reconstructed for the nineteenth century for the first time. It is possible due to the advent of the digitized geomagnetic records in the Helsinki and St. Petersburg observatories. These data have been available since 1844 and 1878, respectively. We assume that the reconstructions are reliable enough to study the solar magnetic field of the past. The polarities inferred for the nineteenth and twentieth centuries display similar sector structures. Seasonal variations of the ratio of positive and negative sectors give clear evidence of solar magnetic field reversals starting from the second half of the nineteenth century.
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 The magnetic field of the Sun stretched out by the solar wind forms the interplanetary magnetic field (IMF). As the Sun rotates, the IMF twists into a spiral shape called the Parker spiral. Originating from the solar magnetic field, the IMF is mostly directed along this spiral either away from or toward the Sun (i.e., positive and negative IMF polarities). In the equatorial plane, it looks like intermittent sectors with opposite IMF polarities or so-called sector structure.
Svalgaard  and Mansurov  independently discovered that the polarity of the IMF can be inferred from the diurnal variation of polar geomagnetic fields (the S-M effect). Later on, Friis-Christensen and Wilhjelm  found that the effect is caused by the Disturbance Polar current powered by the azimuthal Y component (DPY) ionospheric current system. This system is located at polar geomagnetic latitudes in both hemispheres and powered by the azimuthal BYGeocentric Solar Magnetospheric (GSM) component of the IMF. The GSM (Geocentric Solar Magnetospheric) coordinate system is commonly used to define the IMF components. The XZ plane of this system contains the projection of the Earth's magnetic dipole on the plane perpendicular to the Earth-Sun direction (X axis). In the northern polar cap, the DPY current is directed eastward when BY component is positive and westward when negative. So the corresponding geomagnetic variation at high latitudes depends on the sign of the BY. As the IMF is mostly directed along the Parker spiral, the sign of BYstrongly correlates with the IMF polarity. When it is positive, the BYcomponent is also positive; otherwise, it is negative. Figure 1 demonstrates the geomagnetic variation of the horizontal H component at the subauroral station Nurmijarvi in 1982 on the day when BY is positive (A days) and the day when BYis negative (T days). On A days (the red curve), the geomagnetic variation is mostly above the diurnal curve and on T days (the blue curve)—below. Therefore, the effect allows one to infer the type of day, A or T.
 Few techniques to infer the IMF polarities have been proposed so far. The first one was implemented by Svalgaard[1972, 1975]. His method is based on the data from the polar station Thule (87.4oN geomagnetic latitude) and the subpolar Godhavn (78.3oN) and infers polarities back to 1926. Later on, Vennerstroem et al.  found that the IMF polarity could even be inferred from subauroral stations. They additionally used geomagnetic records from two subauroral stations: Sitka (60.4oN) and Sodankyla (64.0oN), where records began in 1905 and 1914, respectively. As the polarities inferred by these two methods are found to be slightly different [Hiltula and Mursula, 2007], we proposed our own technique [Vokhmyanin and Ponyavin, 2012a, 2012b]. It includes a new procedure of deriving the average diurnal curve and a slightly different analysis of the S-M deviations. To extend the time coverage of the polarities inferred, we also used data from three subauroral stations: Sitka, Sodankyla, and Lerwick (61.9oN).
 The S-M effect is more evident in the polar regions where the most part of the DPY current is concentrated. Consequently, the best results with 90% of correct polarities are derived from high-latitude stations. However, as pointed out by Vennerstroem et al. , the influence of the DPY current is significant in a larger range of latitudes. Our results confirmed this suggestion giving 77–79% of correct polarity definitions when using data from subauroral stations. This is very useful for the geomagnetic stations as mid latitudes started to record much earlier than those at high latitudes.
 One of the oldest subauroral station with hourly geomagnetic records available in a digital format is the Helsinki observatory. It is located at 56.59oN. Continuous geomagnetic observations started here in 1844 and were carried out until the beginning of the twentieth century. As pointed out by Nevanlinna [1997, 2004], the digitized Helsinki records are suitable for geomagnetic studies. Another subauroral station was the St. Petersburg observatory located few degrees further east at 56.20oN. Regular magnetic observations started here in 1841 and also stopped at the beginning of the twentieth century. But it is more important that the S-M effect is still visible at these latitudes (Figure 1). Thus, the IMF sector structure has been restored for the first time for the nineteenth century.
2 Data Sets
 Regular hourly magnetic observations started in Helsinki on 1 July 1844. The magnetic elements were declination (D) and the horizontal (H) and vertical (Z) components (for more details, see Nevanlinna ). The H and D data series are now accessible in the digital format through the Finnish Meteorological Institute site (http://www.geo.fmi.fi/MAGN/magn/Helsinki/). Observations of Dand H components are available up to 1895 and May 1897 with large gaps in 1882–1884 and 1891–1892. Due to the disturbances from the nearby electric tramway traffic, most of the observations after 1897 become very noisy and unreliable for magnetic activity studies [Nevanlinna, 2004].
 Magnetic observations in St. Petersburg started in 1841 and were carried out until 1877 (with large gap in 1863–1869), then continued in Pavlovsk located 30 km southeast of St. Petersburg. These geomagnetic records are not completely digitized yet. Currently, we have only H and D data series from 1878 to 1905, though this interval can be extended up to 1841–1911. We assume that the Helsinki and St. Petersburg records were digitized correctly and the difference between the nineteenth and twentieth century measuring instruments is not crucial.
 During the satellite era, geomagnetic observations were carried out at the Nurmijarvi (57.73oN) and Leningrad stations (56.26oN). These data were taken from the Kyoto web site of World Data Center (WDC) for Geomagnetism (http://wdc.kugi.kyoto-u.ac.jp/). As noted by Nevanlinna , diurnal variations of H and Dcomponents are practically identical at both the Nurmijarvi and Helsinki observatories. The same is true for the St. Petersburg-Pavlovsk and Leningrad. This suggests the reliability of the Helsinki and St. Petersburg records and that the configuration of the ionospheric currents over these stations in the nineteenth century was the same as in the twentieth century. Therefore, we can adjust our technique by using the Nurmijarvi and Leningrad data and then apply it to the geomagnetic data in the nineteenth century.
 We also used the daily records of the IMF BYand BXcomponents to estimate the success rate of the method. These satellite measurements are accessible from the OMNI (Operating Missions as a Node on the Internet) database of NASA NSSDC (http://omniweb.gsfc.nasa.gov/).
 The sign of the daily BY component can be defined from the sign of the S-M deviations—the difference between the mean diurnal curve and the daily variation of the H (D) component. Yet we should mention that the S-M effect is not uniform throughout the day. One can see in Figure 1 that the largest difference between variations on A and T days is around midnight and in the morning (21–06 universal time (UT)), while at midday hours the difference is the smallest. During this time, the S-M deviations are rather subtle and thus can be confused with other disturbances. Therefore, it is preferable not to consider such periods.
 Due to the solar extreme ultraviolet radiation, the ionospheric conductivity varies throughout the year. It causes variations in the configuration of the DPY currents and hence in the S-M effect. We estimated typical variations on A and T days for all days within 1966–2005 to understand how the effect varies with season. For each hour of a given day, we find two values. Both are averaged over 55 days (±1 synodic rotation period) but for the different signs of the hourly BY IMF component. Though we get A and T curves and most importantly the difference between them. The latter was superposed over all years to obtain the diagrams in Figure 2. These diagrams allow us to define the periods when the S-M effect is small and to find out how the effect changes from one season to another. Also in certain periods, the difference between A and T curves is negative. This can be seen in Figure 2 as the blue areas. Worst periods for the polarity inferring with less than 60% of the success rate are 08–12 and 19 UT hours. At that time, the S-M effect is small in both the H and Dcomponents. This is more evident from the right plot in Figure 2, where we demonstrate the success rate of the polarity inferring separately for each hour. However, these diagrams also show that the periods of the small S-M effect are not constant and vary throughout the year. At the rest of the time, the sign of the BYcomponent can be estimated quite well. Thus, the overall success rate is about 80% in average per day.
 The S-M deviations now can be determined by the subtraction of the mean diurnal curve. In our method, this curve is defined as an average of the diurnal variations within a certain range of days with almost equal geomagnetic activity. More details of how we find the mean diurnal curve are described in our previous papers [Vokhmyanin and Ponyavin, 2012a, 2012b].
 Finally, the polarity Pd for a given day d is obtained by the following formula:
where the geomagnetic field components (H or D) are denoted by B, the mean diurnal curve values—by D, and w are the weights derived from the diagrams in Figure 2 and allowing us to exclude hours when the S-M effect is small. The results are then corrected in Bartels diagrams by the simple smoothing procedure, described in section 2.3 of Vokhmyanin and Ponyavin [2012a].
 We compare our results with the daily polarities of the IMF from satellites. Considering that most of the time the IMF is directed nearly along the Parker spiral, we define A days when BY>0 and BX<0 and T days when BY<0 and BX>0. Other days (13.6 % of the total number of days) were not taken into account. The success rate is defined as a number of coincidences with the GSM sectors divided by the number of all days. The success rates of the polarity inferring using the Nurmijarvi (NUR) and Leningrad (LEN) data are shown in Table 1. Observations in the Leningrad station stopped in 1988. So the overall success rate using the data from both stations can be estimated only in 1966–1988. It is seen that the success rates for Nurmijarvi and Leningrad are quite similar. The total success rate is about 82%. Therefore, we suggest that our polarity data set is sufficiently reliable.
Table 1. Success Rates and Standard Deviations (in %)
IAGA, International Association of Geomagnetism and Aeronomy
 However, any studies based on such polarity proxies are limited to daily resolution. From the right plot in Figure 2, we see that the hourly success rate is rather low and even drops below 60%. As the method is only a rough model of the S-M effect, it cannot consider all the factors affecting the geomagnetic field. This disadvantage is evident in hourly polarities but disappears when studying daily IMF polarities.
 It is also important to state that the success rate correlates well with the level of the geomagnetic activity. Figure 3 shows that it increases with the geomagnetic activity presented by the aa-index available since 1868. Thus, the reliability of IMF polarity proxies can be roughly estimated from 1868 to the present.
4 Results and Discussions
 The IMF sector structure inferred by our method is shown in Figure 4. The polarities are presented on five Bartels 27 day diagrams according to five solar cycles 9–13 (1844–1901). The red cells mark A days with positive IMF polarity (the IMF is directed mostly along the Parker spiral away from the Sun). The blue cells mark T days. Each row consists of 27 days which is equal to approximately one synodic rotation period. Thus, Bartels diagrams allow one to trace the sector structure evolution from one rotation to another. All the diagrams in Figure 4 demonstrate the predominance of the two sector structure. It is more clearly seen in cycles 10, 12, and 13.
 We can also roughly estimate the periodicity of the sector structure. The patterns with no shifting from one rotation to the next denote periods of 27 days and those shifted by 1 day to the right explicitly denote a 28 day periodicity. The structures with a period of 27 days are mostly observed during the declining phase of solar cycles, while the 28 day periodicity is most commonly observed during the rising phase of solar cycles. The same features can be seen in the satellite era.
 We also checked the overall ratio of A and T days. In 1844–1964, it is about 1.021. The reason for this T dominance is unclear at the moment. One can speculate that negative polarity predominates in the data. Moreover, the same is true for the twentieth century (1.058 in 1965–2012). However, this may be an indication of some artifacts produced by our technique. Table 1demonstrates that T days are slightly more often inferred correctly. Such skewness may also be a cause for the predominance of T days.
 Around the equinoxes (Autumn and Spring), the Earth passes through the high heliographic latitudes (Northern and Southern Hemispheres) with a predominance of one polarity from the corresponding solar hemisphere [Rosenberg and Coleman, 1969]. The effect is called the Rosenberg-Coleman rule. Using the polarity proxies, it is possible to estimate the annual variation in the predominant polarity of the IMF [Wilcox and Scherrer, 1972]. We found the ratios of A and T days to the total number of days separately in Autumn (August–October) and Spring (February–April) (similarly to Hiltula and Mursula ). The results are presented in Figure 5. For 1906–2005, these ratios were obtained using the polarity proxies from our earlier studies [Vokhmyanin and Ponyavin, 2012a, 2012b]. It is well known that the polarity of the solar magnetic field is reversed nearly every 11 years. Therefore, these ratios should look like waves with the same 22 year period but with opposite phases in Autumn and Spring. The strongest dominance of one type of the day, the maxima and minima of these waves, coincides with solar activity minimum (the vertical lines), when the solar magnetic field has the form of axisymmetric magnetic dipole. We also plotted two sine waves with the 22 year period (the blue wave for Autumn and the red for Spring). Their phases were set according to the ratios observed during the satellite period.
 As far back as the 1910s, both waves are clearly visible. In the nineteenth century, the ratios are more complicated, especially in Spring. A possible explanation is that the sector structure for the nineteenth century was reconstructed by using data from only one or two stations at lower latitudes and, therefore, with a lower success rate. However, the waves are still detectable. It means that in the nineteenth century, the solar magnetic field in polar regions also changes its polarity according to a 22 year cycle.
 Thus, the solar magnetic field, which has only been directly observed since 1908 [Hale, 1908], can now be reconstructed as far back as the nineteenth century. The IMF polarities presented in this paper can be found in the Supporting Information files.
 This research was supported by RFBR grant for young scientists (12-02-31531). The authors express their gratitude to Sergey Sokolov who provided us with digitized data of Pavlovsk observatory and to Kirill Krasilnikov who also digitized these data. The authors thank NASA NSSDC for OMNI data of IMF components and WDC for Geomagnetism in Kyoto for providing ground-based data. We are also indebted to the people who digitized Helsinki geomagnetic records.
 The Editor thanks Eigil Friis-Christensen and an anonymous reviewer for their assistance in evaluating this paper.