The study intercompares three stochastic interpolation methods originating from the same geostatistical family: least-squares collocation (LSC) known from geodesy, as well as ordinary kriging (OKR) and universal kriging (UKR) known from geology and other geosciences. The objective of this work is to assess advantages and drawbacks of fundamental differences in modeling between these methods in imperfect data conditions. These differences primarily refer to the treatment of the reference field, commonly called ‘mean value’ or ‘trend’ in geostatistical language. The trend in LSC is determined globally before the interpolation, whereas OKR and UKR detrend the observations during the modeling process. The approach to detrending leads to the evident differences between LSC, OKR and UKR, especially in severe conditions such as far from the optimal data distribution. The theoretical comparisons of LSC, OKR and UKR often miss the numerical proof, while numerical prediction examples do not apply cross-validation of the estimates, which is proven to be a reliable measure of the prediction precision and a validation of empirical covariances. Our study completes the investigations with precise parametrization of all these methods by leave-one-out validation. It finds the key importance of the detrending schemes and shows the advantage of LSC prior global detrending scheme in unfavorable conditions of sparse data, data gaps and outlier occurrence. The test case is the modeling of vertical total electron content (VTEC) derived from GNSS station data. This kind of data is a challenge for precise covariance modeling due to weak signal at higher frequencies and existing outliers. The computation of daily set of VTEC maps using the three techniques reveals the weakness of UKR solutions with a local detrending type in imperfect data conditions.

中文翻译：

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在异质间隔区域 TEC 数据、低阶趋势和异常值发生条件下，通用克里金法中局部去趋势的缺点

该研究比较了源自同一地质统计学家族的三种随机插值方法：大地测量学中已知的最小二乘法 (LSC)，以及地质学和其他地球科学中已知的普通克里金法 (OKR) 和通用克里金法 (UKR)。这项工作的目的是评估这些方法在不完美数据条件下建模的根本差异的优缺点。这些差异主要涉及参考字段的处理，在地统计语言中通常称为“平均值”或“趋势”。LSC 的趋势是在插值之前全局确定的，而 OKR 和 UKR 在建模过程中消除了观察结果的趋势。去趋势化的方法导致了 LSC、OKR 和 UKR 之间的明显差异，特别是在恶劣的条件下，例如远离最佳数据分布。LSC、OKR 和 UKR 的理论比较经常错过数值证明，而数值预测示例不应用估计的交叉验证，这被证明是预测精度的可靠度量和经验协方差的验证。我们的研究通过留一法验证对所有这些方法进行了精确的参数化，从而完成了调查。它发现了去趋势方案的关键重要性，并展示了 LSC 先验全局去趋势方案在数据稀疏、数据缺口和异常值出现的不利条件下的优势。测试案例是对源自 GNSS 站数据的垂直总电子含量 (VTEC) 进行建模。由于较高频率的弱信号和现有的异常值，这种数据对于精确的协方差建模是一个挑战。使用三种技术计算每日 VTEC 地图集揭示了在不完美数据条件下具有局部去趋势类型的 UKR 解决方案的弱点。