The construction of the background covariance matrix is an important component of ionospheric data assimilation algorithms, such as Ionospheric Data Assimilation Four‐Dimensional (IDA4D). It is a matrix that describes the correlations between all the grid points in the model domain and determines the transition from the data‐driven to model‐driven regions. The vertical component of this matrix also controls the shape of the assimilated electron density profile. To construct the background covariance matrix, the information about the spatial ionospheric correlations is required. This paper focuses on the vertical component of the model covariance matrix. Data from five different incoherent scatter radars (ISR) are analyzed to derive the vertical correlation lengths for the International Reference Ionosphere (IRI) 2016 model errors, because it is the background model for IDA4D. The vertical distribution of the correlations is found to be asymmetric about the reference altitude around which the correlations are calculated, with significant differences between the correlation lengths above and below the reference altitude. It is found that the correlation distances not only increase exponentially with height but also have an additional bump‐on‐tail feature. The location and the magnitude of this bump are different for different radars. Solar flux binning introduces more pronounced changes in the correlation distances in comparison to magnetic local time (MLT) and seasonal binning of the data. The latitudinal distribution of vertical correlation lengths is presented and can be applied to the construction of the vertical component of the background model covariance matrix in data assimilation models that use IRI or similar empirical models as the background.

中文翻译：

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电离层垂直相关距离：从ISR数据估算，分析以及对电离层数据同化的影响

背景协方差矩阵的构建是电离层数据同化算法（例如电离层数据同化四维（IDA4D））的重要组成部分。它是一个矩阵，用于描述模型域中所有网格点之间的相关性，并确定从数据驱动区域到模型驱动区域的过渡。该矩阵的垂直分量还控制着被吸收的电子密度分布图的形状。为了构造背景协方差矩阵，需要有关空间电离层相关性的信息。本文着重于模型协方差矩阵的垂直分量。分析了来自五个不同的非相干散射雷达（ISR）的数据，以得出国际参考电离层（IRI）2016模型误差的垂直相关长度，因为它是IDA4D的背景模型。发现相关性的垂直分布关于计算相关性的参考高度是不对称的，在参考高度之上和之下的相关长度之间存在显着差异。发现相关距离不仅随高度呈指数增加，而且具有附加的尾上凸点特征。对于不同的雷达，此撞击的位置和大小是不同的。与磁本地时间（MLT）和数据的季节性分箱相比，太阳通量分箱在相关距离中引入了更明显的变化。