This paper focuses on the retrieval of refractivity fields from GNSS measurements by means of least-squares collocation. Collocation adjustment estimates parameters that relate delays and refractivity without relying on a grid. It contains functional and stochastic models that define the characteristics of the retrieved refractivity fields. This work aims at emphasizing the capabilities and limitations of the collocation method in modeling refractivity and to present it as a valuable alternative to GNSS tomography. Initially, we analyze the stochastic models in collocation and compare the theoretical errors of collocation with those of tomography. We emphasize the low variability of collocation formal variances/covariances compared to tomography and its lower dependence on a-priori fields. Then, based on real and simulated data, we investigate the importance of station resolution and station heights for collocation. Increasing the network resolution, for example, from 10 to 2 km, results in improved a-posteriori statistics, including a 10% reduction in the error statistic for the retrieved refractivity up to 6 km. In addition, using additional stations at higher altitudes has an impact on the retrieved refractivity fields of about 1 ppm in terms of standard deviation up to 6 km, and a bias reduction of more than 3 ppm up to 3 km. Furthermore, we compare refractivity fields retrieved through tomography and collocation, where data of the COSMO weather model are utilized in a closed-loop validation mode to simulate tropospheric delays and validate the retrieved profiles. While tomography estimates are less biased, collocation captures relative changes in refractivity more effectively among the voxels within one height level. Finally, we apply tomography and collocation to test their capabilities to detect an approaching weather front. Both methods can sense the weather front, but their atmospheric structures appear more similar when the GNSS network has a well-distributed height coverage.

本文重点介绍了通过最小二乘搭配从 GNSS 测量中检索折射率场的方法。搭配调整可估计与延迟和折射率相关的参数，而无需依赖网格。它包含函数模型和随机模型，用于定义检索到的折射率场的特征。这项工作旨在强调搭配方法在模拟折射率方面的能力和局限性，并将其作为 GNSS 断层扫描的有价值的替代方案。最初，我们分析了搭配中的随机模型，并将搭配的理论误差与断层扫描的理论误差进行了比较。我们强调与断层扫描相比，搭配形式方差/协方差的低变异性及其对先验视野的依赖性较低。然后，基于真实和模拟数据，我们研究了站点分辨率和站点高度对配置的重要性。例如，将网络分辨率从 10 公里提高到 2 公里，可以改进 a 后验统计，包括将检索到的折射率（高达 6 公里）的误差统计减少 10%。此外，在较高海拔地区使用额外的测站对检索的折射率场的影响约为 1 ppm（标准差可达 6 km），偏差减少超过 3 ppm（可达 3 km）。此外，我们比较了通过层析成像和搭配检索的折射率场，其中 COSMO 天气模型的数据在闭环验证模式下用于模拟对流层延迟并验证检索到的剖面。虽然层析成像估计的偏差较小，但搭配可以更有效地捕获一个高度水平内体素之间折射率的相对变化。 最后，我们应用断层扫描和搭配来测试它们检测即将到来的天气锋面的能力。这两种方法都可以感知天气锋面，但当 GNSS 网络具有均匀分布的高度覆盖时，它们的大气结构看起来更相似。