# Chinese Geomagnetic Reference Field 2020 by the Revised Surface Spline Method
## 3 Results  
### Parameter Determination  
According to Equation (2), the main parameters that determine the accuracy of the revised surface spline model include the truncation order K and the number of grid lattice distribution positions \(N\). Because the total number of grid positions is inversely proportional to the square of the grid interval (R; unit is degree), we calculated root mean square residuals, RMS \(\sigma\), using several different truncation orders K and the grid interval R. Three elements, D, I, and F, are fitted; and X, Y, and Z are calculated by D, I, and F to compare with the results of previous studies. Although we obtained the fitting coefficients using the ordinary least squares method based on all four parts of the geomagnetic data, we focused on the geomagnetic field distribution in China. So we calculated the RMS \(\sigma\) based on the first two parts of the geomagnetic data and the data of 1120 repeat stations; the results are displayed in Table 1.  
When K \(>\) 4, the RMS sharply increased when R \(<\) 3 degrees; so this situation was not included in the consideration, and the values in this situation are not shown in Table 1. From Table 1, we can also see the advantages of the revised surface spline method. The lowest RMS values are 73.94 nT for X, 65.01 nT for Y, and 97.82 nT for Z. As a comparison, we also calculated the RMS residual of IGRF13; the results are 0.1858 degrees for D, 0.1089 degrees for I, and 117.48 nT for F. Usually, the estimated RMS errors of IGRF and WMM are 140-300 and 50-150 nT higher, respectively, in China [7, 41, 42]. In comparison, CGRF2010 by the spheric cap harmonic method has a higher value and a lower convergence rate of the RMS residual. The RMS values are about 101 nT for X, 80.5 nT for Y, and 122 nT for Z when the truncation order is 11, and the convergence rates are about 4 nT for X, 0.2 nT for Y, and 4 nT for Z when the order increases from 1 to 11 [29]. The errors will still increase to about 150 nT for X, 80 nT for Y, 180 nT for Z, and 250 nT for F when using the spheric cap harmonic method to build a 3D geomagnetic model [43]. We also calculated the RMS using the Taylor polynomial method, which can also be used to describe the geomagnetic field in the same area when the truncation order is 8. The RMS is 0.16 degrees for D, 0.10 degrees for I, and 111.31 nT for F. We chose a higher truncation order and a lower grid interval to describe the more complex geomagnetic field spatial structure. So K = 3 and R = 2 degrees were determined as the model parameters. Figure 1: Site distribution for CGRF2020. \(\bullet\) repeat stations, \(\Circle\) stations in neighboring countries, \(\blacktriangle\) geomagnetic observatories, and \(\Delta\) positions where geomagnetic data were calculated from EMM. Figure 2: Cont. After studying the right half of Figure 2 (the spatial distribution of seven elements of geomagnetic anomalies), we find the following:  
1. The anomalies in the declination D and the east component Y are positive in most of North China and East China and are negative in most of West China. There are several positive anomalies located at (42\({}^{\circ}\) N, 118\({}^{\circ}\) E), (40\({}^{\circ}\) N, 107\({}^{\circ}\) E), (40\({}^{\circ}\) N, 83\({}^{\circ}\) E), and (35\({}^{\circ}\) N, 118\({}^{\circ}\) E), with the amplitude up to 10\({}^{\prime}\) for D and up to 100 nT for Y; there are several negative anomalies centered near (42\({}^{\circ}\) N, 122\({}^{\circ}\) E), (40\({}^{\circ}\) N, 110\({}^{\circ}\) E), and (40\({}^{\circ}\) N, 80\({}^{\circ}\) E), with the amplitude up to \(-\)10\({}^{\prime}\) for D and 100 nT for Y. 2. The anomalies in the total intensity F and the vertical component Z are negative in most of China. Several old hard blocks correspond to the distribution of positive anomalies. For example, the anomaly over Sichuan Basin is a positive anomaly located at 28-33\({}^{\circ}\) N, 103-112\({}^{\circ}\) E, with the amplitude up to 100 nT for F and Z.