An improved kernel regression (IKR) method based on an adaptive algorithm and particle swarm optimization is proposed. Considering the limitations of current quality control methods in different regions and on multiple time scales, the kernel regression algorithm is applied to the quality control of surface air temperature observations. Observations of 12 reference stations in Jiangsu from 1961 to 2008 and of 14 regions in China from 2010 to 2014 were selected. The analysis of surface air temperature observations was performed in terms of the mean absolute error (MAE), root mean square error (RMSE), consistency indicator (IOA), and Nash–Sutcliffe model efficiency coefficient (NSC). The results indicate that compared with the traditional IDW and SRT methods, the IKR method has a high error detection rate. Furthermore, the IKR method achieves better predictions and fitting in the single-station and multistation regression experiments in Jiangsu and in the national multistation regression prediction experiment.

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Graph neural networks (GNN) is a method to extract spatial information between adjacent nodes. But it cannot extract spatial information between nodes that are far apart. In this paper, to address this issue, we assume that the spatial features between any two nodes are random variables that follow certain distributions, and the variances of the random variables increase as the expectations increase. And we set out the conditions that the random variable should satisfy. This approach has three benefits: 1) Being able to fit the spatial relationships of long-distance nodes. 2) Improving the robustness of the model. 3) Improvement on the most basic GNN model means that this method can be applied to any other GNN models. The experiments on real-world datasets demonstrate the superiority of the model.

Most of the quality control applications of hydrological data are based on basic quality control methods such as logical detection, extreme value check and spatial consistency check. Although these methods can detect problem data with large errors, this makes the data lack credibility. Therefore, a single station data quality control method, SFA-WZLM, is proposed in this paper. This method uses slow feature analysis (SFA) to extract external forcing factors for embedding in chaotic local prediction models. Observations from January 1987 to October 2015 was used as the train set, and observations from December 2015 to October 2017 were used as the test set. The results indicate that the method has higher prediction accuracy than the prediction model without embedded external forcing factors, weighted first-order local prediction model (WFLM) and weighted first-order local prediction model (SFA-WFLM) including external forcing factors and exhibited the best quality control error detection. In addition, the method shows good stability in 6 different climates and different terrain stations across the country in China.