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Verification of the geomagnetic field models using historical satellite measurements obtained in 1964 and 1970
Earth, Planets and Space volume 74, Article number: 187 (2022)
Abstract
In 2019, the World Data Center for SolarTerrestrial Physics in Moscow digitized the archive of observations of the Earth’s magnetic field carried out by the Soviet satellites Kosmos49 (1964) and Kosmos321 (1970). As a result, the scientific community for the first time obtained access to a unique digital data set, which was registered at the very beginning of the scientific space era. This article sets out three objectives. First, the quality of the obtained measurements is assessed by their comparison with the IGRF model. Second, we assess the quality of the models, which at that time were derived from the data of these two satellites. Third, we propose a new, improved model of the geomagnetic field secular variation based on the scalar measurements of the Kosmos49 and Kosmos321 satellites.
Graphical Abstract
Introduction
The history of low Earth orbit (LEO) satellite missions designed to measure the geomagnetic field began with the launch of the Sputnik3 mission on May 15, 1958 in accordance with the scientific program of the International Geophysical Year (IGY). With a payload of 968 kg, this satellite was equipped with the instruments for more than ten different experiments. They included a unique magnetically oriented saturablecore magnetometer (Dolginov et al. 1961), which made it possible for the first time to carry out orbital measurements of the total intensity of the geomagnetic field. In 1959, thanks to the efforts of colleagues from the United States the second satellite Vanguard3 carrying proton magnetometer on board for measuring the total field was launched (Cain 1971). The first spaceborne vector measurements of the geomagnetic field appeared only 20 years later in the MAGSAT mission. As a result, valuable data for a 6month period between 1979 and 1980 became widely available, which made it possible to construct reliable models of the geomagnetic field (Mandea 2006).
At the same time, scalar observations obtained before 1979 are also of apparent scientific interest, though such recordings were almost unavailable to a wide community until recently. Through the efforts of Krasnoperov et al. (2020), unique magnetometer data from the satellites Kosmos49 (operated from October 24 to November 3, 1964) and Kosmos321 (operated from January 20 to March 13, 1970) were digitized and for the first time published electronically online. Kosmos49 carried proton precession magnetometers and Kosmos321 was equipped with a quantum magnetometer; both were used for absolute measurements. During the same period of 1965–1971, the satellites of the POGO series (Polar Orbiting Geophysical Observatories) were also operational. In particular, OGO2, OGO4, and OGO6 satellites provided scalar magnetic field measurements (Jackson and Vette 1975) and OGO data were used to derive main field models, including the International Geomagnetic Reference Field (IGRF) for 1965 (Cain et al. 1967). The magnetic data collected by these satellites are available from DTU website (https://www.space.dtu.dk/english/Research/Scientific_data_and_models/Magnetic_Satellites). Such historical data provide wide opportunities for retrospective analysis of the geomagnetic field in terms of both internal and external sources.
This paper is devoted to the quality assessment of the historical satellite measurements from Kosmos49 and Kosmos321 satellites by comparison with the IGRF model for 1964–1970. In addition, we present a comparison of the direct satellite observations with several models from IZMIRAN (Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation named after N.V. Pushkov of the Russian Academy of Sciences) of those years, which were based on the same observations. Finally, we present new core geomagnetic field models for 1964 and 1970 based on Kosmos49 and Kosmos321 measurements and demonstrate their advantages over existing analogues.
Comparison of direct satellite measurements with IGRF
As noted above, the first satellite measurements of the geomagnetic field were scalar, that is, they measured not the field vector (projections onto three orthogonal axes), but only its modulus (total field or intensity). Two proton magnetometers PM4 were mounted on board of the satellite Kosmos49, the sensors of which were oriented at the right angle. The instruments were switched on by turns from a time program device of high accuracy in the intervals of 32.76 s. The time marks gave the possibility to tie board readings out of each instrument to the absolute time. The magnetometer sensors were mounted at 3.3 m distance from the satellite centre by means of a boom. A small magnetic influence of the satellite at this distance was compensated by a system of permanent magnets, mounted on the bottom of the boom, creating the uniform compensating field in the places of the sensor mountings. The compensation accuracy of the magnetic and electromagnetic influence of the satellite was verified by the absence of modulate effects in the board magnetograms when the satellite rotated around the vertical and horizontal axes by means of a special nonmagnetic device. It was also checked by means of an outer stationary magnetometer when the satellite moved translationally relative to the magnetometer. The accuracy of compensation was about 2 nT. The magnetometer accuracy during the search of an unknown field was from 2 to 3 nT. To avoid errors while measuring the nuclear precession frequency, special arrangements were taken to minimize the satellite angular velocities during its separation from the rocket (Dolginov et al. 1970).
Kosmos321 satellite was equipped by quantum cesium magnetometer QCM1. This is a selfgenerating type magnetometer using the cesium vapor optical pumping method. The correspondence of the QCM1 readings to the absolute values in the range of measured fields was checked by comparison with the proton magnetometer readings. The correspondence was within 2 nT. A special thermal control system ensured the normal functioning of the spectral lamp and absorption chambers outside the satellite's thermal container. The magnetometer sensors were placed in a container, which was removed from the satellite body using a boom 3.6 m long. Nevertheless, the experiment revealed the effect of deviation caused mainly by the influence of thermal currents in the elements of the boom and container fasteners. Due to the rotation of the satellite, the deviation influence represented modulations with the period of the satellite's rotation. These effects were excluded during data processing. The program for the primary computer processing of the experimental data provided the following: conversion of the measured values into magnetic field units, determination of the satellite coordinates at the time of measurement, determination of the theoretical field at the measurement points, and determination of the difference between the measured and calculated field values (Dolginov 1978). The effect of thermal currents was reproduced on the fasteners similar to that of Kosmos321. This interference manifested as a gap in measured values and coincided with the times of switches between the sensors. For this reason, the catalog (Dolginov et al. 1976) contains data for only a limited number of orbits, a total of 5000 measurements, for which the interference had approximately sinusoidal form and was eliminated from data upon data processing.
Mathematical models enable analytical calculation of geomagnetic field components and modulus at any point in space outside the geomagnetic field sources, where the geomagnetic field is a potential field. There are some limitations, however, as models derived from scalar measurements only are subject to the socalled “Backus effect” (Backus 1970). This effect is essentially a strongly erroneous recovery of the internal geomagnetic vector field due to nonuniqueness of the inversion based on total intensity data only. However, properly constructed models make it possible to compare the modelled total field with the directly measured value. Being the reference model of the core field, IGRF is adopted by the international scientific community in geomagnetic studies. It represents a set of coefficients used for the expansion of the geomagnetic potential in spherical harmonics. Each set of coefficients describes a field averaged over a 5year interval, starting at epoch 1900.0. The model is updated every 5 years and the latest, 13th generation IGRF for the period 1900–2020 is available today (Alken et al. 2021a). The obtained coefficient sets guarantee smooth variability of the geomagnetic field over the entire period assuming their linear change between the neighboring epochs. To assess the quality of satellite measurements carried out more than half a century ago, it seems natural to compare them with the predicted values according to the IGRF model, calculated for the corresponding epochs.
The IGRF models include the spherical harmonic coefficients up to order and degree of 10 for 1900–1995 and 13 for 2000–2020, so it describes only the variable internal sources of the geomagnetic field. Therefore, for an accurate comparison of the modelled and measured values, the signal of the external origin should be corrected as much as possible from the raw geomagnetic data. In this regard, we select for comparison only measurements that were obtained on the night side of the Earth, from 22:00 to 05:00 local time, and for geomagnetically quiet periods defined by the values of the planetary geomagnetic activity indices Kp ≤ 2 and Dst < 20 nT. A total of 3766 measurements are selected based on these criteria out of 17,449 values recorded by the Kosmos49 satellite. Withdrawal of the highlatitude measurements affected by auroral electrojets is not applicable, since the maximum latitude of the Kosmos49 flight was ± 50°. The positions of the Kosmos49 satellite when measuring the selected values are shown in Fig. 1a.
The field according to the IGRF model is calculated for October 29, 1964 (epoch 1964.826), the middle of the flight of the Kosmos49 satellite. Figure 2a shows a histogram of the distribution for the differences in the total intensities derived from the IGRF model and directly measured by the Kosmos49 satellite. Difference bins of 10 nT are plotted horizontally, and the probability density calculated for the number of measurements with such differences is plotted vertically. This histogram can be approximated by the Gaussian distribution function with a mean of 2.78 nT and a standard deviation (SD) of 32.83 nT (Table 1). Evident erroneous measurements (80 ones) producing residuals of more than 150 nT (see Fig. 2a) are excluded. Their possible reasons include instrumental failures (e.g., Soloviev et al. 2018), poor processing of raw data and catalogue publishing errors.
To analyze the Kosmos321 data, we select 710 measurements out of 4910, and calculate the IGRFbased field for February 22, 1970 (epoch 1970.144). Here, in addition to the selection criteria used for Kosmos49 measurements we discard data obtained at geomagnetic dipole latitudes higher than 60° in both hemispheres. It permits to avoid systematic and strong distortion of the core field signal by external fields of magnetospheric and ionospheric origin. The positions of the Kosmos321 satellite when measuring the selected values are shown in Fig. 1b. Figure 2b shows a histogram of the distribution of the differences between the selected Kosmos321 measurements and modelled total field values. This histogram is modelled by a Gaussian distribution function with a mean of 13.64 nT and a SD of 26.65 nT (see Table 1).
Figure 3 shows the spatial distribution of the residuals as a function of latitude. Due to the small orbit inclination of the Kosmos49 satellite (49°), most of the time it was located on the night side of the Earth in the northern hemisphere, as evidenced in Fig. 3a. The selected measurements from the Kosmos321 satellite with an orbital inclination of 71° are more evenly distributed between geomagnetic dipole latitudes 60° S and 60° N (Fig. 3b). At the same time, one may observe an expected increase in residuals when the satellite approaches the poles, which is due to intense electromagnetic processes typical for the polar ionosphere. In addition, the spatial distribution of the Kosmos321 residuals (Fig. 3b) is slightly skewed toward positive values in the northern hemisphere, which is likely the reason for the biased mean of the Kosmos321 residuals (see Table 1).
To figure out how well the IGRF model approximates Kosmos49 and Kosmos321 data, we calculate the same statistics for OGO6 (active years 1969–1971), Magsat (1979–1980), Oersted (1999–2008), and SwarmA (since 2013) residuals. Recall that Kosmos49 was operational 11 days in autumn 1964, which fell on the solar activity minimum between 19 and 20th cycles, and Kosmos321 was operational 53 days in winter–spring 1970, which fell on the solar activity maximum of the 20th cycle. To be consistent with the time intervals, seasons and solar cycle phases (Adhikari et al. 2019) corresponding to selected Kosmos measurements, we consider the following data from the listed satellites:

1.
OGO6: 11.01.1970–22.01.1970, central epoch 17.01.1970 (solar maximum);

2.
Magsat: 19.02.1980–08.04.1980, central epoch 15.03.1980 (solar maximum);

3.
Oersted: 19.10.2005–09.12.2005, central epoch 14.11.2005 (almost solar minimum); and

4.
SwarmA: 18.11.2020–29.11.2020, central epoch 24.11.2020 (solar minimum).
For statistics calculation, we apply the same data selection criteria as for Kosmos321 and derive IGRFbased field at the specified central epochs. The results are as follows:

1.
OGO6: mean = − 3.6 nT, SD = 18.1 nT;

2.
Magsat: mean = − 0.3 nT, SD = 9.7 nT;

3.
Oersted: mean = − 1.0 nT, SD = 13.9 nT; and

4.
SwarmA: mean = − 6.4 nT, SD = 11.5 nT.
The statistics do not vary dramatically between all the considered satellites (see figures above and Table 1), although the mean and SD for Kosmos321 are slightly larger than for all the other satellites, and the SD for Kosmos49 is larger than for all the more recent satellites. Still, these results indicate that the IGRF model quite satisfactorily approximates geomagnetic field observations made by the Kosmos49 and Kosmos321 satellites.
Verification of historic models of the geomagnetic field
The initial analysis of the Kosmos49 and Kosmos321 measurements resulted in the analytical models of the geomagnetic field, which are listed in the corresponding catalogs (Dolginov et al. 1967, 1976). The Gauss coefficients of these two models at 1964.0 (hereinafter “M1”) and 1970.0 (hereinafter “M2”) epochs are presented in Appendix 1. Below we provide their comparison with the IGRF model, which, as shown in the previous section, approximates direct geomagnetic field observations quite well. An apparent approach for comparison is estimating the difference between the individual components of the geomagnetic field vectors calculated using two models. For correct comparison, hereinafter the IGRF expansion is limited by the order and degree that are maximum for the considered models.
Figure 4 shows a map of differences in the vertical component (Z) of the core geomagnetic field according to the M1 model and the IGRF model for the corresponding date. Similarly, Fig. 5 shows the result of comparing the M2 model with the IGRF model. Such comparison method is used when evaluating candidate models for IGRF (Alken et al. 2021b). The largest deviations are observed in the equatorial area and reach more than 1000 nT in absolute value, which is an unacceptable error in the study of the geomagnetic field and its secular variation reaching several tens of nT per year. The large spatial differences between the two models (in both Figs. 4 and 5), which are caused by errors in the sectorial terms of the spherical harmonic expansions, are a wellknown manifestation of the Backus effect (Stern and Bredekamp 1975) unaccounted in models M1 and M2. Despite large discrepancies in the Z component, the total intensities from the Kosmos49 satellite are approximated by M1 and IGRF models with an accuracy of about 30 nT (for M1 model SD is 25.56 nT with a mean of 0.47 nT). The discrepancies in the total field between the Kosmos321 measurements and M2 predictions are characterized by a SD of 74.20 nT with a mean of 10.10 nT (see Table 1).
The availability of geomagnetic field models at several neighboring epochs makes it possible to estimate its secular variation (SV). As before, here we compare the SV of the Z component according to different models. Figure 6 shows a comparison of the SV obtained as the difference between the M2 and M1 models divided by the corresponding time interval (about 6 years) with the SV derived from the IGRF model for the period of 1965–1970. Because of the Backus effect, the SV obtained by differencing models M2 and M1 is expected to have very large errors at low latitudes ranging from − 300 to 300 nT/year. These errors of periodic structure arise from large differences in the SV coefficients starting with degree n = 3 between the IGRF and M1/M2 models. Large discrepancies are also observed in the Arctic region and at the coast of Antarctica around Greenwich. For the rest of the Earth's surface the SV from the M1 and M2 models is fairly close to the values according to the IGRF model.
A new geomagnetic field model based on satellite data
The availability of only scalar data obviously complicates the procedure for reconstructing the total magnetic field vector. The concomitant Backus effect mentioned above can be eliminated by adding the knowledge of the accurate location of the magnetic dip equator (Khokhlov et al. 1997). Its minimization is basically gained in one of three ways:

1.
Adding relevant vector data especially collected in the equatorial belt (e.g., Cain et al. 1967);

2.
Adding observations of the position of the equatorial electrojet (Holme et al. 2005); and

3.
Taking into account the position of the dip equator derived from the reference model (UltréGuérard et al. 1998).
For reducing the Backus effect, we follow the third way as the IGRF model is available for 1964 and 1970. Using this model, we determine the dip equator position at each degree of the longitude for the middle of each satellite operation period. To construct a magnetic field model, we adopt an approach from (UltréGuérard et al. 1998) and minimize the function
Here M is the number of measurements, \({B}_{i}\) are the values of the measured total field, \({\mathbf{r}}_{i}\) are the points at which the measurements were made, \(B({\mathbf{r}}_{i};g,h)\) is the total field value according to the model with a set of Gauss coefficients \({g}_{nm},{h}_{nm}\), \(w({\mathbf{r}}_{i})\) is a weighting factor aimed to balance the different density distribution of the measurements over the Earth’s surface, N is the number of points \({\mathbf{r}}_{j}\) defining the dip equator, \(Z({\mathbf{r}}_{j};g,h)\) is the Z component value according to the model at those points and \({w}_{\text{eq}}\) is the weight applied to the dip equator constraint. For a LEO satellite with a maximum trajectory latitude \({\theta }_{\mathrm{max}}\), the weighting factor \(w({\mathbf{r}}_{i})\) chosen as \(\sqrt{{\mathrm{sin}}^{2}{\theta }_{\mathrm{max}}{\mathrm{sin}}^{2}\theta }\) takes into account the fact that most of the measurements are concentrated near the latitudes \({\pm \, \theta }_{\mathrm{max}}\). For the sparse measurements, the weighting factor can be omitted. As for \({w}_{\text{eq}}\), the result of minimization is practically independent of this factor within a wide range (two orders of magnitude). In our calculations, we take \({w}_{\text{eq}}\) equal to 100.
The actual minimization is carried out by the builtin function lsqnonlin () of the Matlab package, which enables solving nonlinear leastsquare (nonlinear datafitting) problems. The minimization method is iterative. The subsequent step of minimizing the function \(S(x)=\frac{1}{2}{\sum }_{i}{f}_{i}^{2}\left(x\right)\) is performed in the twodimensional subspace of the parameter space spanned by the gradient of the function \({g}_{k}={\sum }_{i}{f}_{i}\frac{\partial {f}_{i}}{\partial {x}_{k}}\) at a given point and the Newtonian step n, which is determined from the system of equations:
A function in a twodimensional subspace is approximated by a quadratic form. If the next calculated step leads to a decrease in the function value, then follows the next iteration. If not, the admissible step decreases, and the procedure is repeated. Calculation stops when the admissible step becomes small enough. As an initial approximation, the values of the coefficients \({g}_{nm},{h}_{nm}\) are chosen according to the IGRF model at the beginning of 1965 and 1970.
To calculate the coefficients based on the Kosmos49 (hereinafter referred to as the “N1” model) and Kosmos321 (hereinafter, the “N2” model) data, we apply selection criteria weaker than those used for comparing measurements with the IGRF model (see "Comparison of direct satellite measurements with IGRF" section). This is due to the extremely small set of raw measurements, especially those obtained by the Kosmos321 satellite; if they are filtered according to the criteria specified in "Comparison of direct satellite measurements with IGRF" section, we get vast regions of Africa, Europe and Canada that are not covered by data at all (see Fig. 1b).
Thus, when selecting data from the Kosmos49 satellite, the time filter is removed (both dayside and nightside data are used) and only the criteria Kp ≤ 2 and Dst < 20 nT are applied. We also discard the evident erroneous measurements visible on the histogram in Fig. 2a as bars on the left and right for residuals of more than 150 nT. As a result, 12,511 out of 17,499 measurements are used for building the N1 model. Mean and SD of the differences between the N1 model and the actual observations are 0.23 nT and 27.57 nT, respectively (see Table 1). Maps with plotted positions of the Kosmos49 satellite when taking the measurements selected for the N1 model are shown in Fig. 7a.
As for the Kosmos321 satellite, we also consider both dayside and nightside data (see argumentation above). We apply the geomagnetic dipole latitude filter glat < 60° and weakened criteria Kp ≤ 3 and Dst < 50 nT to select the data for the model calculation. As a result, 2510 out of 4910 measurements remain; their spatial distribution is shown in Fig. 7b. Mean and SD of the differences between the N2 model and the actual observations are − 1.07 nT and 11.34 nT, respectively (see Table 1). The coefficients of the resulting two models are listed in Tables 2, 3.
The comparison of the N1 and N2 models with the IGRF model (Z component) for 1964 and 1970, respectively, is shown in Fig. 8. An expected degradation in the data approximation by the N2 model is observed in the southern part of the African continent and geomagnetic pole regions (Fig. 8b), where original data are missing (see Fig. 7b). Nevertheless, as compared to M1 and M2 models, N1 and N2 deviations from the IGRF predictions are reduced significantly.
An improvement in the SV prediction for the 1964–1970 period can be traced by comparing the discrepancy between the M1/M2 and IGRF models (Fig. 6) with the discrepancy between the N1/N2 and IGRF models. Figure 9 shows a map for the latter case, limited to ± 60° in latitude due to the same limitation for the initial data selection for the N2 model. The SV according to the new models becomes more realistic in the eastern part of the Pacific Ocean, African continent and the vast region of Southeast Asia (see Figs. 6 and 9). The variance in SV predictions between N1/N2 and IGRF models is reduced to [− 40, 40] nT/year, except for South Africa, where it reaches 60 nT/year due to lack of Kosmos321 data (see Figs. 7b and 8b). We estimate the SV predicted by different models more in detail in the next section.
To quantify the discrepancies between IGRF, M1,2 and N1,2 models we might compare their power spectra in terms of mean square field averaged over a spherical surface against each harmonic degree (e.g., Lowes 1966, 1974). Figure 10 displays a spectrum for each considered model as well as the spectrum of the difference between each pair of models: IGRF and M1, IGRF and N1, IGRF and M2, IGRF and N2 at Earth mean radius (6371.2 km). It follows that the total square error in the N1 and N2 field models is minimal for both 1964 and 1970.
Comparison of the model predictions with observatory data
For additional validation of the constructed models, it is useful to employ highprecision groundbased observations of the geomagnetic field provided by magnetic observatories. Though their geographic coverage is uneven (Kozyreva et al. 2019), the main value of the observatory data is continuity and long duration of the full magnetic vector observations at a fixed point in space. These data are widely used for both external (Petrov and Krasnoperov 2020) and internal field studies. In particular, it makes it possible to study the SV of the geomagnetic field and use these data as calibrating values for satellite observations and derived models. Today, the quality standards for such data and observatories are specified by the INTERMAGNET global network (Love and Chulliat 2013). A complete data archive from magnetic observatories over the entire history of observations is available online at the World Data Center for Geomagnetism in Edinburgh (http://www.wdc.bgs.ac.uk/).
To validate the IGRF, M1, M2, N1 and N2 models, we select data from nine midlatitude observatories from both hemispheres for the period 1955–1980, which overlaps the considered years 1964, 1965 and 1970. The data from nearequatorial and highlatitude observatories are not considered due to the higher impact of external magnetic fields caused by equatorial and polar electrojets. A map with the location of the selected observatories is shown in Fig. 11.
First, we linearly interpolate data gaps in original hourly values available at the webportal of the World Data Center. Then, we derive monthly means from hourly values using the running average over 30day window. Despite different completeness and quality of the data at different observatories for the period under consideration, nevertheless, the data presented are quite representative for evaluating model predictions. We compare them with the modelled values of the Z component at the observatory locations for 1964/1965 and 1970. Figure 12 shows how they fit to the continuous series of the Z component measured at the observatories.
For some of the considered observatories (CLF, FRD, VIC, GNA) the data are corrected for the local crustal anomalies (also known as observatory biases), which were quantified using recent highquality satellite data (Verbanac et al. 2015). Unfortunately, the biases are unknown for the rest of considered observatories (MMB, TKT, PAF, HER, PIL). Table 4 contains SV values for Z component derived from IGRF, M1/M2 and N1/N2 models by simple subtraction of 1964/1965 value from 1970 value divided by number of years in between, and their absolute deviations from SV based on observatory data (ΔSV). The observatorybased SV is calculated as a difference between 1970 and 1964 yearly means divided by number of years in between.
For most of the observatories the actual SV is very wellfitted by the new N1/N2 models, despite large differences in quantity and spatial distribution between selected Kosmos49 and Kosmos321 data (see Fig. 7). Moreover, in some cases (MMB, CLF, GNA and PAF) the SV is even better traced by the new models rather than IGRF model, according to ΔSV values from Table 4. The worst data approximation by the new models is observed around 1970 at HER observatory (South Africa), which is due to the highest discrepancies between the N2 model and IGRF in this region (see Figs. 8b and 9).
In a number of cases, there is a high consistency between all three models, as, for example, for the FRD (USA) or HER (South Africa) observatories in 1964. However, the majority of plots presented in Fig. 12 contain unacceptable outliers produced by M1 and M2 model predictions, which makes them inapplicable for studying the SV over the considered period.
Conclusions
The efforts undertaken by (Krasnoperov et al. 2020) have made it possible for the first time to access and process digital arrays of the historical satellite observations of the total field in 1964 and 1970. Up to now, these data along with OGO series observations represent the earliest spaceborne measurements of the geomagnetic field available online.
The high consistency between the direct geomagnetic field measurements by the Kosmos49 and Kosmos321 satellites and the modelled total intensity according to the IGRF model indicates the high quality of these historical data. This argues for their applicability for scientific research and makes them unique and valuable material for retrospective study of the geomagnetic field dynamics.
Comparison of the historical models of the core geomagnetic field based on the Kosmos49 (model M1) and Kosmos321 (model M2) data with another historical model for the year 1960 based solely on ground and marine observations (including those carried out at the famous nonmagnetic schooner Zarya) (Adam et al. 1963, 1964) suggests that the transition to the use of satellite measurements provided significant improvement in the geomagnetic field modelling for the regions, where groundbased data were insufficient, namely, in the oceans and the Antarctic zone. However, it is shown, that the models M1 and M2 are clearly affected by the Backus effect, which makes them inapplicable in studying the core magnetic field dynamics.
The main value of analytical models for the core geomagnetic field expansion into spherical harmonics is the ability not so much to calculate the instantaneous characteristics of the field, but to estimate its variability over time, i.e., the SV. We present new models based on the data from the Kosmos49 (model N1) and Kosmos321 (model N2) satellites that take into account the Backus effect. As a result, these models much better fit the actual 1964–1970 SV derived from the groundbased observations than M1 and M2 models based on the same satellite data. The results predicted by N1 and N2 are satisfactory despite big differences in quantity and spatial distribution between 1964 and 1970 data sampling points used for their construction.
For some of the groundbased observation sites, the proposed N1 and N2 models approximate the SV even better than the IGRF model. This suggests that the inclusion of Kosmos49 and Kosmos321 data into the IGRF model for the period 1964–1970 is not complete. However, for the regions, where raw satellite data are not available, the new model predictions are still poor.
Availability of data and materials
Kosmos49/321 satellite data are available at World Data Center for SolarTerrestrial Physics in Moscow (https://usd.wdcb.ru/indexen.html) and PANGAEA data repository (https://doi.org/10.1594/PANGAEA.907927). OGO6, Magsat, Oersted, and Swarm satellite data are available at https://www.space.dtu.dk/english/Research/Scientific_data_and_models/Magnetic_Satellites. The observatory data are available at the World Data Center for Geomagnetism in Edinburgh (http://www.wdc.bgs.ac.uk/), INTERMAGNET (http://intermagnet.org) and Interregional Geomagnetic Data Center (http://geomag.gcras.ru).
Code availability
The developed software is not available online.
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Acknowledgements
The results presented in this paper use data collected at the INTERMAGNET magnetic observatories (http://intermagnet.org). We express our gratitude to the national institutes that support them, INTERMAGNET community for promoting the high standards of magnetic observatory practice, the ISC World Data System (https://www.worlddatasystem.org/) and the Interregional Geomagnetic Data Center (http://geomag.gcras.ru) for making the data available online. The facilities of the GC RAS Common Use Center “Analytical Center of Geomagnetic Data” (http://ckp.gcras.ru) were used for conducting the research. The authors wish to thank two anonymous reviewers for the valuable comments, which helped to improve the material presentation. In addition, the authors are grateful to Dr. Roman Krasnoperov from GC RAS for providing rare information on the Kosmos technical specifications.
Funding
The research was carried out with the financial support of the RFBR, MOST (China) and DST (India) as a part of the scientific project No. 195580021 (AS) and in the framework of budgetary funding of the Geophysical Center RAS, adopted by the Ministry of Science and Higher Education of the Russian Federation (DP).
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AS set the problem, elaborated the research scheme and wrote the text. DP did programming and generated figures. Both authors read and approved the final manuscript.
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Soloviev, A.A., Peregoudov, D.V. Verification of the geomagnetic field models using historical satellite measurements obtained in 1964 and 1970. Earth Planets Space 74, 187 (2022). https://doi.org/10.1186/s40623022017495
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DOI: https://doi.org/10.1186/s40623022017495