Many modern outer radiation belt models simulate the long‐time behavior of high‐energy electrons by solving a three‐dimensional Fokker‐Planck equation for the drift‐ and bounce‐averaged electron phase space density that includes radial, pitch‐angle, and energy diffusion. Radial diffusion is an important process, often characterized by a deterministic diffusion coefficient. One widely used parameterization is based on the median of statistical ultralow frequency (ULF) wave power for a particular geomagnetic index Kp. We perform idealized numerical ensemble experiments on radial diffusion, introducing temporal and spatial variability to the diffusion coefficient through stochastic parameterization, constrained by statistical properties of its underlying observations. Our results demonstrate the sensitivity of radial diffusion over a long time period to the full distribution of the radial diffusion coefficient, highlighting that information is lost when only using median ULF wave power. When temporal variability is included, ensembles exhibit greater diffusion with more rapidly varying diffusion coefficients, larger variance of the diffusion coefficients and for distributions with heavier tails. When we introduce spatial variability, the variance in the set of all ensemble solutions increases with larger spatial scales of variability. Our results demonstrate that the variability of diffusion affects the temporal evolution of phase space density in the outer radiation belt. We discuss the need to identify important temporal and length scales to constrain variability in diffusion models. We suggest that the application of stochastic parameterization techniques in the diffusion equation may allow the inclusion of natural variability and uncertainty in modeling of wave‐particle interactions in the inner magnetosphere.

中文翻译：

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计算ULF波径向扩散模型中的变异性

许多现代的外部辐射带模型通过求解三维Fokker-Planck方程来模拟高能电子的长期行为，该方程针对漂移和反弹平均电子相空间密度，包括径向，俯仰角和能量扩散。径向扩散是一个重要过程，通常以确定性扩散系数为特征。一种广泛使用的参数化基于特定地磁指数Kp的统计超低频（ULF）波功率的中位数。我们对径向扩散进行了理想的数值集成实验，通过随机参数化将扩散系数随时间和空间的变化引入其基础观测的统计特性所约束。我们的结果证明了长时间内径向扩散对径向扩散系数的全部分布的敏感性，突出表明仅使用中值ULF波功率会丢失信息。当包括时间可变性时，合奏表现出更大的扩散，扩散系数变化更快，扩散系数的变化更大，并且尾部较重。当我们引入空间可变性时，所有整体解集的方差随着较大的空间可变性尺度而增加。我们的研究结果表明，扩散的变化性会影响外部辐射带中相空间密度的时间演化。我们讨论了确定重要的时间尺度和长度尺度以限制扩散模型中变异性的需求。