The geomagnetic vector field consists of components such as “total magnetic force”, “declination angle”, “inclination angle”, “horizontal partial force”, and “vertical partial force”. The declination represents the deflection of the magnetic north (north pointed to by a magnetic compass) from the true north (the geographic north on a map). Although the true north is more relevant in everyday life, it is usually difficult to sense straightforwardly. As the magnetic north can easily be determined using a compass, the magnetic north is rather useful for indirectly pointing the true north by referring to a given value of the location's declination.

In the case of geomagnetic observations, the azimuth – defined hereafter as the horizontal angle (clockwise positive) of a direction of interest with respect to the true north – must be determined by an independent method. One is the traditional astronomical method using a celestial body at night. In this method, which has been revitalized because of its high accuracy (see Barazzetti, 2025), the horizontal angle between an azimuth mark and a reference star, such as Polaris, is measured. Horizontal and elevation angles of the reference star in the equatorial coordinate system are provided by a celestial orbit calculation software. The predicted angle can then be combined with the observed angles to calculate the azimuth of the azimuth mark. The same method has also been applied to the sun in many observatories (Jankowski and Sucksdorff, 1996), although it is difficult to achieve a comparable accuracy due to the difficulty of centering of the sun with its much larger appearance and quicker motion.

Alternatively, Global Navigation Satellite Systems (GNSS) can be used to determine the azimuth. By measuring positions at two points by GNSS precisely, the azimuth of one point with respect to the other can be calculated. The positioning accuracy is generally known to be a few millimeters (Static mode), less than 1 m (Differential GPS), and more than a few meters (Single mode). Static mode provides the most accurate positioning accuracy; however, it requires extended observation times and two sets of equipment, which increases costs. Single mode is economical since it requires only one piece of instrument, but it has the disadvantage of lower accuracy because systematic errors such as atmospheric delay are typically not corrected. Differential GPS achieves higher accuracy than single mode by obtaining correction data for systematic errors based on Continuously Operating Reference Station data. However, the accuracy of the correction data degrades depending on the distance from the reference station, and in any case, its accuracy is inferior to static mode. In terms of the azimuth, the reported accuracy is about a few arcseconds (e.g. Lalanne et al., 2013). The INTERMAGNET technical reference manual (Bracke, 2025) recently updated suggests to apply Differential GPS, or otherwise the traditional astronomical observation, when redetermination is necessary.

Japan Meteorological Agency has adopted the method using Polaris at its magnetic observatories, Kakioka, Memambetsu and Kanoya, that are registered as the INTERMAGNET observatories (Love and Chulliat, 2013). It has been aware, however, that there are difficulties with this method. First of all, it is subject to weather conditions, with the Polaris sighting being easily precluded by clouds. Particularly, rain clouds make the observation totally infeasible. Furthermore, for an even more accurate observation of Polaris, the optimal season is restricted to late Autumn, when the star migrates vertically rather than horizontally during the typical observation hours in the early evening. These timing limitations make the opportunities of the observation fewer. While this is actually not a major problem at Kakioka which has permanent staff, it significantly matters for Memambetsu and Kanoya, which are unmanned observatories visited by observers only once every two weeks for maintenance work and the absolute measurement. Table 1 presents the number of azimuth observations made at each observatory during the recent observation period from 2022 to 2024. As indicated in the table, while Kakioka conducts approximately 10 observations annually, Memambetsu and Kanoya conduct only a few observations each year. Under the current methodology, increasing these to a level equivalent to Kakioka is difficult. Another difficulty is the extra labor inevitable for the staff to make the azimuth observation with Polaris, for which they have to work overtime after their normal office hours when the sky is sufficiently dark. This requirement is especially burdensome for the staff visiting Memambetsu and Kanoya. There is only one observer for each, travelling all the way there by car accompanied by a supporting member. Obviously, it would be preferable if they had much more chance for the azimuth observations during the daytime.

The Sun-based azimuth method, which is applied by many observatories, can address daytime operation but remains weather-dependent like the Polaris method and is typically less accurate. While methods for improving accuracy have been developed (e.g., Rasson et al., 2017), achieving the required accuracy of a few arcseconds remains challenging. Practical constraints also arise because observation pillars are typically located indoors and lack windows that enable constant viewing of the sun; our site can view Polaris but not the Sun, so the Sun-based method may be infeasible for such observatories.

Given the circumstances above, we investigate the azimuth observations by GNSS in view of its potential to alleviate the difficulties of our conventional observation. We compare the accuracy of the azimuth observations by GNSS and the Polaris sighting, in order to assess if our conventional observations can eventually be replaced by the GNSS observations, especially at Memambetsu and Kanoya. To this end, we conducted an experiment at Kakioka to investigate general performance of the GNSS approach with reference to our requirement in the precision for the absolute measurement. This paper is organized as follows. In Sect. 2, starting with an overview of the GNSS observation method, we give detailed description of individual observations and the data processing method. Also, the precision of the azimuth resulting from the GNSS observations is presented. In Sect. 3, the difference between the azimuth obtained by GNSS and Polaris sighting is discussed. Section 4 summarizes the entire report.

To compare the accuracy and precision of the azimuth observations by GNSS and Polaris sighting, let us first introduce our conventional observations at Kakioka. Annually around October, the observations are performed independently by as many observers as ten, where a single observer sights Polaris eight times. Figure 7 shows the azimuth values derived from the Polaris observations at the Kakioka since 1997. The true azimuth obtained from Polaris observation is defined as follows, based on the average of the annual observation results. First, the results for each year are averaged after excluding obvious outliers. Subsequently, a comparison is made between this average value and the previous year's average to ascertain whether a substantial change has occurred. If the value has not changed significantly, we determine that the true azimuth has remained constant from the previous year. The mean value for the year 2024 is estimated to be approximately 0°32^′53^′′. Furthermore, we define the true azimuth from 2011 to 2024 as 0°32^′55^′′. While there are apparently variances in the results among the observers, the standard deviation of the azimuth by Polaris sighting is usually less than 3 arcsec.

The current experiment reveals that the azimuth by GNSS (θ2 in Table 2) is smaller by about 10 arcsec than that by Polaris sighting. The difference is unlikely attributable to the observation error, considering the high precision of each observation indicated by their standard deviations as small as a few arcseconds.

What is the cause of this significant difference? Here we will consider Deflection of the Vertical (DoV), which is well known in the field of geodetic surveying (see Vittuari et al., 2016; and the references therein). DoV is defined as a deviation angle between the direction of gravity and the geometric normal to the reference ellipsoid's surface at a given location. The measurement of an angle with the traditional instruments, such as total stations and theodolites, is based on local direction of the gravity, while GNSS observations are based on the ellipsoidal normal. As illustrated in Fig. 7, azimuths obtained from the Polaris and GNSS observations can differ if the plumb line differs from the ellipsoidal normal.

Atumi (1933) first reported DoV in Japan. According to his investigation at Tsukubasan which is roughly 10 km west of Kakioka (Table 1 of Atumi, 1933), the astronomical latitude and longitude are 36°13^′22.0^′′ N and 140°5^′55.0^′′ E, respectively, while the geodetic latitude and longitude are 36°13^′22.3^′′ N and 140°5^′67.2^′′ E, respectively. The east-west component of DoV η can be estimated by η=λa-λgcos⁡φg, where λa is the astronomical longitude and φg and λg are the geodetic latitude and longitude, respectively. Using the values reported by Atumi (1933), the η turns out to be -9.8 arcsec. The effect of the DoV η on the difference δ between the azimuth by the GNSS and Polaris observations can be estimated by applying the level correction equation (cf. Kakioka Magnetic Observatory, 1987) δ=btan⁡h, where b is the tilt of the instrument and h is the altitude angle of Polaris (as illustrated in Fig. 8b). Assuming that b is represented by η (Fig. 8a) at Tsukubasan, δ is about 7 arcsec, which roughly explains the observed difference between the azimuth by the Polaris and GNSS observations. For a more rigorous verification, observation or calculation of the very local DoV at Kakioka would be necessary, as the instrument tilt b can still be somewhat different from the DoV at Tsukubasan η.

Another potential source of systematic error is positioning deviation during the installation of the GNSS receiver. However, this deviation is typically within a few millimeters, which is too small to account for the errors obtained in this study. In addition, although not documented in this paper, a separate observation conducted in the previous year yielded nearly identical systematic errors. Consequently, it is more natural to consider an underlying cause.

While the azimuth observation – the measurement of deflection angle of an azimuth mark with respect to the true north – is essential for the absolute measurement at magnetic observatories, the method with star sighting is associated with difficulties due to weather-dependent observation conditions, as well as demands for overtime work into the evening. A way to mitigate these hardships would be introducing an alternative method with GNSS observation. To examine the applicability of the GNSS technique to the azimuth observations especially at our unmanned observatories, Memambetsu and Kanoya, an experiment is conducted using the GNSS technique at Kakioka in 2024. Under the setting of observation necessarily including horizontal angle measurements at eccentric points (Sect. 2), the precision of the azimuth of the azimuth mark is found to be a few arcseconds, which is comparable to that derived from previous Polaris observations. A significant difference of about 10 arcsec is revealed between the two methods. This is due most likely to the DoV, according to the azimuth deviation predicted by using a report of measurement plumb line direction acquired at a distance of roughly 10 km to the west. It indicates a necessity of further investigation, such as an in-situ observation of the DoV. Determining whether the azimuth by GNSS or the one by Polaris is absolutely accurate is difficult. This is because it depends on assumptions about the shape of the Earth. Is it an irregular geoid shape or an ellipsoid? However, when considering geomagnetic modelling, maintaining continuity with past observational results is likely more important. Therefore, when transitioning to the GNSS method, we believe that by determining the DoV at each observatory and adding it to the GNSS results, we can connect to the past Polaris results.

Our transition to GNSS has only recently begun to be considered. In transitioning to the method with GNSS, it will also be necessary to consider even more efficient procedure for these tasks; in this experiment the series of work consisted of an hour of GNSS observations, 30 min horizontal angle observations, calculations, and preparation of the equipment. In the future, surveys are planned for Kanoya and Memanbetsu, where efficient azimuth observations are of the utmost importance. It is anticipated that the transition to GNSS will commence with these two observatories.