The Van Allen radiation belts in the magnetosphere have been extensively studied using models based on radial diffusion theory, which is derived from a quasi‐linear approach with prescribed inner and outer boundary conditions. The 1D diffusion model requires the knowledge of a diffusion coefficient and an electron loss timescale, which is typically parameterized in terms of various quantities such as the spatial (L) coordinate or a geomagnetic index (e.g., Kp). These terms are typically empirically derived, not directly measurable, and hence are not known precisely, due to the inherent nonlinearity of the process and the variable boundary conditions. In this work, we demonstrate a probabilistic approach by inferring the values of the diffusion and loss term parameters, along with their uncertainty, in a Bayesian framework, where identification is obtained using the Van Allen Probe measurements. Our results show that the probabilistic approach statistically improves the performance of the model, compared to the empirical parameterization employed in the literature.

中文翻译：

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使用Van Allen探针的拟线性径向扩散参数的贝叶斯推断

已经使用基于径向扩散理论的模型对磁层中的Van Allen辐射带进行了广泛研究，该模型是从具有规定的内部和外部边界条件的准线性方法得出的。一维扩散模型需要了解扩散系数和电子损耗时标，通常根据各种量（例如空间（L）坐标或地磁指数（例如K p）。这些术语通常是凭经验得出的，不能直接测量，因此由于过程固有的非线性和可变的边界条件而无法精确知道。在这项工作中，我们通过在贝叶斯框架中推断扩散和损失项参数的值及其不确定性来演示一种概率方法，在该方法中，使用Van Allen Probe测量值进行了识别。我们的结果表明，与文献中采用的经验参数化相比，概率方法在统计学上提高了模型的性能。