Random error in remotely sensed (RS) and modeled soil moisture (SM) products is typically assumed to be statistically stationary for the purpose of SM merging applications. In reality, such error is often non-stationary, which may undermine applications based on a stationary assumption. Here, we introduce a dual time-space (2D) SM merging approach that considers a class of inferred error that is non-stationary and undetectable in time (or space) but stationary and detectable in space (or time). Such 2D merging is realized in a least-squares framework where spatial and temporal error variances for each product are estimated via a triple collocation (TC) analysis. As a test case, a 2D-merged SM product is obtained by combining three independent SM products – including two RS SM products and one modeled SM product. Results show that the 2D merging method can effectively handle non-stationary errors and, as a result, produces a superior merged SM product than classical 1D merging methods. The spatial and temporal correlations with in-situ observations are 0.62 and 0.63 [−] on average for 2D merging methods, and 0.58 and 0.59 [−] on average for classical 1D merging methods. By providing a more effective way to detect and remove non-stationary errors during the process of merging multi-source SM products, this approach will improve future global multi-source merged SM products.

遥感 (RS) 和模拟土壤水分 (SM) 产品中的随机误差通常被假定为统计平稳，以便 SM 合并应用程序。实际上，这种误差通常是非平稳的，这可能会破坏基于平稳假设的应用程序。在这里，我们引入了一种双时空 (2D) SM 合并方法，该方法考虑了一类在时间（或空间）上非平稳且不可检测但在空间（或时间）中静止且可检测的推断误差。这种 2D 合并是在最小二乘框架中实现的，其中通过三重搭配 (TC) 分析估计每个产品的空间和时间误差方差。作为测试用例，通过组合三个独立的 SM 产品（包括两个 RS SM 产品和一个建模的 SM 产品）获得 2D 合并 SM 产品。结果表明，二维合并方法可以有效地处理非平稳错误，因此比经典的一维合并方法产生更好的合并 SM 产品。二维合并方法与原位观测的空间和时间相关性平均为 0.62 和 0.63 [-]，经典一维合并方法平均为 0.58 和 0.59 [-]。通过提供一种更有效的方法来检测和去除多源SM产品合并过程中的非平稳错误，该方法将改进未来的全球多源SM产品合并。对于经典的一维合并方法，平均为 59 [-]。通过提供一种更有效的方法来检测和去除多源SM产品合并过程中的非平稳错误，该方法将改进未来的全球多源SM产品合并。对于经典的一维合并方法，平均为 59 [-]。通过提供一种更有效的方法来检测和去除多源SM产品合并过程中的非平稳错误，该方法将改进未来的全球多源SM产品合并。