面向稀疏散布数据集的时空Kriging优化

时空Kriging法通过将变异函数向时空域进行扩展得到时空变异函数,有效地利用时空邻近的采样点综合进行插值,由于时空稀疏散布数据集具有单一时刻下样本点数量少以及时空分布不规律的特点,难以满足使用时空Kriging插值法的基本条件,导致插值精度不高,据此本文提出了优化方法：通过多时段叠置拟合空间变异函数的方法,综合利用时空邻域内的采样点以解决单一时刻下空间邻域内数量不足情况;控制时间变异对空间变异函数拟合的误差影响;采用积合式模型构建时空变异函数进行插值。最后使用Argo海温数据进行插值实验,在相同条件下与时空Kriging法以及时空权重法的交叉验证结果对比得出,该方法在保证拟合所需采样点数量要求的同时,有效削减了一般时空Kriging法中时间变异对空间变异函数拟合结果的干扰,插值结果的绝对误差均值从0.5降低至0.2以内,稳定性进一步增强,改善了时空Kriging法在稀疏散布数据条件下精度上的不足。

An Improved Spatio-temporal Kriging Algorithm to Sparse Scattered Dataset

Spatio-temporal Kriging is efficiently used in interpolation by adjacent sampling point in space-time. The core is to extend the spatial variogram into space time. Because sparse scattered dataset is lack of sampling point in single time slice and the distribution of point is non-uniform, we propose an improved method of spatio-temporal Kriging against low precision. First, the trend surface of the sample is obtained by using cubic polynomial. The sample data is decomposed into trend terms and residual terms, because original trending sample data can't satisfy the stationary assumption required for Kriging interpolation. Then, the time variogram is fitted with less data coming from a nearby stationary station. The sampling position of the stationary station is constant and the sampling frequency is consistent. It is suitable for fitting the variogram because its observation sequence is longer, although few in quantity. Meanwhile,instead of fitting method by dataset in all-time, we adopt the strategy of multi-period overlap fitting to obtain a more reasonable spatial variogram. The length of the time segment is selected according to the degree of time variation. The variable values of the sampling point in each sub-period are calculated and overlaid to fit spatial variogram. In such way, the spatio-temporal variogram is constructed based on product-sum model, which is used to estimate the variable value in space and time. In final phrase, interpolation is performed using the spatio-temporal weights solved by Kriging equations. To verify the effectiveness of the proposed method, a comparison with the existing interpolation method is made by sea temperature data of Argo buoys from China Argo real-time data center and moored buoys from Pacific Marine Environmental Laboratory. From the comparison of the cross-verification results of interpolation, we judge the accuracy and stability of the method based on MAE and MSE. Compared to general spatio-temporal kriging and spatio-temporal weight interpolation, the proposed method is increased by 69.5% and 38.9% respectively in accuracy, and increased by 61.9% and 48.9% respectively in stability. The proposed method is improved based on spatio-temporal Kriging, considering the structural characteristics and spatial and temporal variation characteristics of sparse scattered datasets. Spatio-temporal variogram is more scientific and practical, which is constructed through the proposed method. Interpolation precision and stability are also improved significantly.