摘要：We develop a new methodology for the multi-resolution assimilation of electric fields by extending a Gaussian process model (Lattice Kriging) used for scalar field originally to vector field. This method takes the background empirical model as “a priori” knowledge and fuses real observations under the Gaussian process framework. The comparison of assimilated results under two different background models and three different resolutions suggests that (a) the new method significantly reduces fitting errors compared with the global spherical harmonic fitting (SHF) because it uses range-limited basis functions ideal for the local fitting and (b) the fitting resolution, determined by the number of basis functions, is adjustable and higher resolution leads to smaller errors, indicating that more structures in the data are captured. We also test the sensitivity of the fitting results to the total amount of input data: (a) as the data amount increases, the fitting results deviate from the background model and become more determined by data and (b) the impacts of data can reach remote regions with no data available. The assimilation also better captures short-period variations in local PFISR measurements than the SHF and maintains a coherent pattern with the surrounding. The multi-resolution Lattice Kriging is examined via attributing basis functions into multiple levels with different resolutions (fine level is located in the region with observations). Such multi-resolution fitting has the smallest error and shortest computation time, making the regional high-resolution modeling efficient. Our method can be modified to achieve the multi-resolution assimilation for other vector fields from unevenly distributed observations.
