Method Of Natural Orthogonal Components Research Articles

Construction of the spatial-temporal model of the main geomagnetic field using satellite data

The spatial-temporal model of the geomagnetic field has been constructed using the data of the high-accuracy survey of the CHAMP German satellite, obtained during its operation from May 2001 to September 2007. The daily average spherical harmonic models calculated at an interval of four days are used as initial data in order to expand these models by the method of natural orthogonal components (NOCs). It has been indicated that the obtained NOC series rapidly converges. The secular variations, secular acceleration, and Dst variation are distinguished as individual NOC components, which makes it possible to construct the spatial-temporal field model. In addition, the models-predictions have been constructed for the year 2008 based on the candidate models of the main field and the secular variation for the year 2005, which were used to obtain the IGRF2005 international model. A comparison of the models-predictions with the model constructed for the year 2008 using our method indicated that the accuracy of our model is not lower than that of the models, obtained by other scientific groups using the traditional method.

Statistical characteristics of the day‐to‐day variability in the geomagnetic Sq field

Day‐to‐day variability in the geomagnetic Sq field is studied by using the magnetic data from a meridian chain of magnetometers along 120°E longitude. The method of natural orthogonal components (NOC or eigenmode analysis) is applied to separate the Sq variation from complicated disturbances. The first eigenmode with the largest eigenvalue represents fairly well the Sq variation with a conspicuous day‐to‐day variability in the daily range. For the stations on the same north‐ or south‐side of the Sq current system focus, the day‐to‐day variations show a positive correlation. In contrast, for the stations on the different sides of the Sq focus, they show a negative correlation, suggesting an important role of latitudinal shift of the Sq current system focus to the day‐to‐day variability in the Sq daily range. The Sq daily range is correlated with the magnetic indices Ap and Dst in a peculiar way: On some severe disturbed days, noticeable enhancements of the Sq are observed, implying increases in the ionospheric conductivities and/or tidal wind velocities; on other severe disturbed days, however, dramatically reduced Sq variations occur, suggesting dominant effects of the “disturbance dynamo” process.

The Evolution Characteristics of Geomagnetic Disturbances During Geomagnetic Storm

AbstractWith the data of the geomagnetic meridian observatories in China, 25 geomagnetic storms in the period of 1997 to 1999 have been analyzed by using three kinds of methods which are the method of Natural Orthogonal Components (NOC), Correlation analysis and Fourier analysis. Three steps have been adopted to decompose the storm‐time variation (Dst) relating to the universal time (UT), the solar daily variation (Sq) and the disturbance‐daily variation (SD) depending on the local solar time (LT). The results indicate that (1) The spatial distribution and the temporal evolution characteristics of equatorial symmetric ring current are reflected clearly by the Dst variation. (2) The amplitude of Sq reaches the maximum or the minimum during most main phases in MZL, BMT and QGZ observatories, reflecting the variation of the geomagnetic field with the movement of the Sq focus on latitude. (3) During the main phase, the amplitude of SD reaches the maximum, decreasing slowly in the recovery phase. (4) Correlation analysis and Fourier analyses are effective techniques to extract the variations of Sq and SD.

Decomposition of daily geomagnetic variations by using method of natural orthogonal component

In this paper the method of natural orthogonal components (NOC) is utilized to decompose the daily magnetic variation, expressing the variation as a summation of the eigenmodes. The results show that the first and second NOC eigenmodes represent the solar quiet daily variation, Sq, and the disturbance‐daily variation, SD, respectively. The third and fourth eigenmodes may be related to specific currents in the magnetosphere. Remarkable day‐to‐day (DTD) variations exist in the amplitudes of the eigenmodes. The combination of the eigenmodes reproduces the complicated characteristics in the DTD variation of the daily magnetic variation. The decomposition of the daily magnetic variation presented in this paper is helpful for understanding the mechanism of the daily variation and its DTD variation. In addition, this decomposition method provides a ground‐based monitoring of the current systems in several important regions of the near‐Earth space.

NOC model of the earth’s main magnetic field

The method of natural orthogonal components (NOC) is used to analyze the earth’s main magnetic field IGRF 1900–2000, and the NOC model of the field is established. The first step of the analysis is to calculate eigen modes of the field from the Gauss coefficients of IGRF 1900–2000. Then the magnetic field for each epoch is expanded in a series at the basic function set constructed by the eigen modes, and the intensity coefficients of the eigen modes are calculated. Test of the convergency and stability of the NOC model shows that the model has very short series and much rapid convergency in comparison with the conventional spherical harmonic models of IGRF. Comparison of the eigen modes obtained from different IGRF model groups indicates that the low-degree eigen modes are rather stable, while the high-degree modes show a relatively large variability. The physical meaning of the eigen modes in the NOC model is discussed, and an interesting relationship is found between the spatial structure of the main field and its secular variation.

Natural orthogonal component analysis of International Geomagnetic Reference Field models and its application to historical geomagnetic models

SUMMARY The International Geomagnetic Reference Field (IGRF) models for 1900‐2000 are analysed by means of the method of natural orthogonal components (NOC), and are expressed in the form of NOC series. The obtained NOC series approaches the original IGRF models very rapidly, and therefore the magnetic field can be very well approximated by the first few terms of the NOC series. This feature of the NOC series makes it possible to upgrade the truncation level ¯ N of historical magnetic models by calculating high-degree Gauss coefficients from the existing low-degree ones. Using the main-field models IGRF 1900‐2000, we calculated the principal components of the magnetic field. Each of the components has a specific spatial structure and a varying intensity. The structures of the principal components are rather stable for different periods. Consequently, we can safely assume that the magnetic field just before 1900 consists of the same components, but with different intensities. Taking the model for 1885 (truncation level ¯ N = 6) as an example and solving a linear equation system, we calculated the high-degree Gauss coefficients (n = 7‐10) from the existing low-degree coefficients (n = 1‐6). Adding this model to the model series of IGRF 1900‐2000, we will obtain an extended model series for 1885‐2000 with a common truncation level ¯ N = 10. Repeating this procedure, we will obtain a model series extended backward to early ages.

The dependence of winter aurora on interplanetary parameters

The dependence of the northern winter aurora on interplanetary parameters is examined for images obtained from the Polar spacecraft Ultraviolet Imager (UVI) during the month of January 1997. Linear correlation analysis is used to relate auroral brightness to interplanetary parameters as a function of magnetic latitude (MLAT) and magnetic local time (MLT). Spatial maps of maximum magnitude correlation coefficient and optimal lag times are presented. In addition, the Method of Natural Orthogonal Components (MNOC) is applied to UVI images and an orthogonal set of eigenmodes of auroral behavior is produced. The dominant eigenmodes are determined to be (1) the main auroral oval brightness, (2) polar cap contraction/expansion, (3) dawn/dusk aurora, and (4) midnight sector brightening/quenching. The temporal coefficients for the various eigenmodes are correlated separately with solar wind parameters and interplanetary magnetic field (IMF) components. The dominant influence of the negative Bz component is confirmed, but the timescale of its influence is found to vary widely. The MNOC procedure allows some of the more subtle relationships between the aurora and the interplanetary parameters to be isolated, particularly those associated with the solar wind density and IMF Bx and By.

Revision of the high-degree Gauss coefficients in the IGRF 1945–1955 models by using natural orthogonal component analysis

The high-degree Gauss coefficients (n ≥ 7) in the IGRF models for 1945–1955 exhibit some unusual and unreliable behaviors in comparison with the models for other epochs. In this paper the method of Natural Orthogonal Components (NOC) is used to revise these coefficients. The obtained result shows that the main geomagnetic field can be approximated very well by the first a few NOC eigen modes. The high-degree Gauss coefficients (n ≥ 7) are deduced for each of IGRF models using the first 6 eigen modes and low-degree Gauss coefficients (n ≤ 6). The deduced high-degree coefficients are in very good agreement with the original ones for all models except those for 1945, 1950 and 1955. In comparison with the unusual behaviors in the IGRF1945–1955 models, the deduced high-degree coefficients for these models exhibit fairly smooth time-variations. Besides, the magnetic energy and magnetic flux calculated by the revised Gauss coefficients show more continuous secular variations and consistent characteristics.

The equatorial counter electrojet: Part of a worldwide current system?

The method of natural orthogonal components was applied to the ground geomagnetic data in the Central Asian sector (72–83°E), during the summer months of 1995, in an attempt to identify additional current systems that are superposed on the normal Sq current vortex and related to the equatorial counter electrojet (CEJ). The principal components, when examined in equivalent current representation, provide useful insights into the behavior of ionospheric current systems on different days. Statistical analyses performed in the present work suggest a possible relationship between the CEJ field and the noontime D variation observed at low latitudes. The results are in conformity with an earlier global simulation model.

An improved method to deduce the unloading component for magnetospheric substorms

Because our earlier analysis [Sun et al., 1998] confirmed that the directly driven component prevails during the growth phase, an attempt has been made in this paper to deduce the unloading component as accurately as possible. First, the directly driven pattern is determined by taking the average of patterns of the equivalent current function during the growth phase of substorms, then the correlation method is applied to calculate time variations of the magnitude of the directly driven component. Next, the method of natural orthogonal components is used to analyze the residual part, which equals the difference between the total current and the directly driven component. In the present method, the pattern and the magnitude of the unloading component are much improved. The correction in the magnitude of two components is ∼ 50%. Time variations of the magnitude of the unloading component thus obtained will be crucial in understanding the unloading process. The effect of the variable directly driven pattern, which is ∼ 11% of the magnitude of the directly driven component, also has been estimated quantitatively. This improved method has the advantage of allowing study of individual substorms over the earlier method.

Mathematical separation of directly driven and unloading components in the ionospheric equivalent currents during substorms

This paper attempts to separate objectively the directly driven and unloading components in substorm processes by applying the method of natural orthogonal components (MNOC). A time series of the ionospheric equivalent current function with time resolution of 5 min during March 17–19, 1978 is calculated on the basis of six meridian chains magnetometer data during the International Magnetospheric Study in order to obtain the fundamental orthogonal basis set. The first and second natural components of the set thus obtained dominate over the rest of the natural components. The first natural component is found to have a two‐cell pattern, which is well known to be associated with global plasma convection in the magnetosphere. It is enhanced during the growth phase and expansion phase of substorms and decays during the recovery phase of substorms. Further, it is in fair correlation to the ϵ parameter with time lag of 20–25 min. This can be identified as the directly driven component. The second natural component reveals itself as an impulsive enhancement of the westward electrojet around midnight between 65° and 70° latitude during the expansion phase only. It is much less correlated with the ϵ parameter than the first one. Thus, as a first approximation, we identify it as the unloading component. It is shown that the directly driven component tends to dominate over the unloading component except for a brief period soon after substorm onset. This is the first clear determination of the time profile of the unloading component.

Using Satellite Magnetic Survey Data for Spatial-Temporal Modeling of the Geomagnetic Secular Variation

The method of natural orthogonal components (NOC) analysis, which separates temporal variations, and spherical harmonic analysis, which models spatial distribution, were combined to model the spatial-temporal variations of the geomagnetic field over the globe. NOC's obtained in this way describe the temporal variations year by year without smoothing. Use of combined observatory and satellite magnetic survey data for developing a spatial-temporal model of equal accuracy on the globe and over the time interval of the data is proposed.

An Evaluation of a Regional Orthogonal Field Model for Canada with Respect to the Canadian Geomagnetic Reference Field

Regional spatial-temporal models of the geomagnetic field have been produced by a variety of techniques. Recently, spherical cap harmonic analysis has gained wide acceptance as a means of modelling the magnetic field over a portion of the globe. Time variations of the field are commonly represented by polynomials or trigonometric series. The Canadian Geomagnetic Reference Field for 1995 (CGRF) is an example of a model produced in this manner. There are, however, other techniques that may offer advantages for some applications. The method of natural orthogonal components is one of these. To demonstrate this method, a spatial-temporal model of the geomagnetic field changes over Canada (ROM-Canada) has been produced using North American observatory annual means and Canadian repeat station data. These data were fitted with rectangular Legendre polynomials using natural orthogonal components as the temporal functions. Overall, total-intensity first-differences computed from the CGRF and ROM-Canada model the observed first-differences with comparable accuracy. ROM-Canada appears to be somewhat more accurate in the centre of the modelling area, but less accurate near the edges. Moreover, the ROM-Canada models of the vector components are less accurate than the CGRF.

Determination of the latitude of Sq focus and its relation to the electrojet variations

The latitude of the Sq focus is determined analytically using the method of natural orthogonal components. Geomagnetic data along the 75°E meridian have been used. The day-to-day variations of the latitude of the Sq focus thus determined are very highly correlated with the electrojet enhancements. The strength of the normal Sq field and the electrojet field are not correlated. It appears that as the Sq focus moves towards the equator the entire current pattern bodily moves equatorwards with an increased current concentration in the electrojet region.