Data Assimilation of High‐Latitude Electric Fields: Extension of a Multi‐Resolution Gaussian Process Model (Lattice Kriging) to Vector Fields
Data Assimilation of High‐Latitude Electric Fields: Extension of a Multi‐Resolution Gaussian Process Model (Lattice Kriging) to Vector Fields
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DOI：
10.1029/2021sw002880
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发表时间：
2021-12
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影响因子：
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通讯作者：
Haonan Wu;Xian Lu
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作者：
Haonan Wu;Xian Lu
通过将原来用于标量场的高斯过程模型（格点克里格）扩展到矢量场，发展了一种新的多分辨率电场同化方法。该方法将背景经验模型作为“先验”知识，在高斯过程框架下融合真实的观测值。在两种不同背景模式和三种不同分辨率下的同化结果的比较表明：（a）与全局球谐拟合（SHF）相比，新方法显著降低了拟合误差，因为它使用了适用于局部拟合的限幅基函数;（B）拟合分辨率由基函数的数目决定，是可调的，分辨率越高，误差越小，这表明捕获了数据中的更多结构。我们还测试了拟合结果对输入数据总量的敏感性：（a）随着数据量的增加，拟合结果偏离背景模型，并且变得更多地由数据决定;（B）数据的影响可以到达没有数据的偏远地区。同化也比SHF更好地捕捉当地PFISR测量的短周期变化，并与周围保持一致的模式。通过将基函数归属到具有不同分辨率的多个水平（精细水平位于具有观测值的区域中）来检查多分辨率格型克里格。这种多分辨率拟合具有最小的误差和最短的计算时间，使区域高分辨率建模变得高效。我们的方法可以修改，以实现多分辨率同化其他矢量场的非均匀分布的观测。
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.