We calculated and analyzed variation of the non-dipole(ND)magnetic field at the millennium scale over the Chinese mainland during 2000 BC–1900 AD using the newest global geomagnetic model,CALS3K.4(3K.4).The newest-generation IGRF(IGRF11)was used to verify the results.Taking component Z for example,we calculated and analyzed the distribution and annual change rates of the ND field during 1900–1990 AD every 5 yr,using two models.To thoroughly analyze the contributions of field sources,quadrupole and octupole fields,and others within the ND field at the surface and core-mantle boundary(CMB)were investigated.Results show that there were three main variation phases of the field during the period 2000BC–1900 AD.The mean amplitude roughly reflected the ND field because of the distribution and variation of that field,corresponding somewhat to the mean amplitude change.A magnetic anomaly of the ND field over East Asia(EA)first emerged in 1682 AD,and its extreme intensity had increased a total of 15276.95 nT by 1900 AD.Its location moved continuously southeastward after 1690 AD.The asymmetry between location and intensity of extreme points over EA,particularly during1740–1760 AD,indicates irregularity of fluid motion inside the outer core.Mean annual changes of Z are generally divided into four phases,which first oscillated between 2000 and 800 BC,then increased,decreased and increased in the periods 800BC–300 AD,300–900 AD and 900–1900 AD,respectively.The intensity of mean annual change increased a total of 22.87nT/yr.Anomaly extreme locations based on 3K.4 and IGRF11 over EA centered around 44°N and 103°E for degree(n)greater than 5,and intensities continuously increased with n.During 2000 BC–1990 AD,ND energy of Z at the surface and CMB had decreased in total by 18.29%and 23.23%,respectively.The field source of 26–210 pole fields are more or less affected by the lithospheric field.Energies of higher degree at the surface attenuate by almost 99%compared with CMB,but mean attenuation speeds of the low-
The selection of the truncation level （TL） and the control of boundary effect （BE） are critical in regional geomagnetic field models that are based on data fitting. We combine Taylor and Legendre polynomials to model geomagnetic data over China's Mainland for years 1960, 1970, 1990, and 2000. To tackle the TL and BE problems, we first determine the range of TL by calculating the root-mean-square error （RMSE） of the models. Next, we determine the optimum TL using the Akaike information criterion （AIC） and the normalized root- mean-square error （NRMSE）. We use the regional anomaly addition （RAA） and the uniform addition （UA） method to add supplementary point outside the national boundary, and find that the intensities of extreme points gradually decrease and stabilize. The UA method better controls BEs over China, whereas the RAA method does a better job at smaller scales. In summary, we rely on a three-step method to determine the optimum TL and propose criteria to determine the optimum number of supplementary points.
