Assessment of Three-Dimensional Interpolation Method in Hydrologic Analysis in the East China Sea

Abstract

The water mass in the East China Sea (ECS) shelf has a complicated three-dimensional (3D) hydrologic structure. However, previous studies mostly concentrated on the sea surface based on the sparse in situ and incomplete satellite-derived observations. Therefore, the 3D interpolation technology was introduced for the reconstruction of hydrologic structure in the ECS shelf using in situ temperature and salinity observations in the summer and autumn of 2010 to 2011. Considering the high accuracy and good fitness of the radial basis function (RBF) methods, we applied the RBF methods to the in situ observations to completely reconstruct the 3D hydrologic fields. Other 3D interpolation methods and 2D methods were also tested for a comparison. The cubic and thin plate spline RBFs were recommended because their mean absolute error (MAE) in the 10-fold cross-validation experiments maintained the order of ~10−2. The 3D RBF reconstructions showed a reasonable 3D hydrologic structure and extra details of the water masses in the ECS shelf. It also helps evaluate regional satellite-derived sea surface temperature (SST). Comparisons between the interpolated and satellite-derived SST indicates that the large bias of satellite-derived SST in the daytime corresponds to weak mixing during low-speed wind and shows seasonal variation.

Application of Trigonometric Polynomial Fitting Method in Simulating the Spatial Distribution of PM2.5 Concentration in South-Central China

“…The functions of RBF interpolation methods include Gaussian functions, multi-quadratic functions, inverse quadratic functions, and thin-plate splines. Among these, the RBF interpolation method combining cubic and thin-plate spline functions has proven to be an effective approach for reconstructing ECS shelf temperature and salinity with minimal errors [29]. Therefore, we chose the thin-plate spline RBF interpolation method for subsequent experiments.…”

“…Spatial interpolation methods, widely employed in atmospheric studies and other fields, offer a solution by mitigating the impact of insufficient ground-based observation data on accurately characterizing the spatial and temporal distribution characteristics of PM 2.5. These methods include spatiotemporal statistical models based on Kriging interpolation, spatial and temporal regression models based on Kriging interpolation integrated with remote-sensing AOD data, neural network models based on RBF interpolation, and 3D RBF interpolation for hydrological structure analysis [22][23][24][25][26][27][28][29][30].…”

“…Zheng Haiming and Shang Xiaoxiao developed a neural network model based on RBF interpolation, which exhibits superior predictive performance compared to traditional backpropagation models and offers distinct advantages in PM 2.5 prediction [28]. A study of the hydrological structure in the ECS by applying 3D RBF interpolation was carried out by Gao et al in 2022, which showed that 3D RBF successfully reconstructed a reasonable 3D hydrological structure in the ECS shelf [29]. In 2023, Li Yuhan et al employed the RBF interpolation method to calculate the density of fracture distribution.…”

3D spatial distribution of soil pollutants based on geo-shadowing anisotropic RBF-PCA

“…Based on a comparative analysis involving 1982 cases and 29 different interpolation methods, Franke concluded that multiple quadratic RBF interpolation outperforms most other interpolation techniques. Today, RBF interpolation is employed extensively in contemporary geography, such as in the investigation of toxic substance distribution near mining areas, analysis of spatial distribution patterns of pollutants, and precipitation allocation within polluted sites (Ding et al, 2018;Qiao et al, 2019;Yang and Xing, 2021;Gao et al, 2022). The RBF interpolation method was chosen for this study due to several key advantages, such as efficient solutions to linear equations, easy extension into three dimensions, ability to offer smooth interpolation of scattered data, and adept handling of discrete spatial and temporal data (Carr et al, 2001;Fasshauer, 2007;Macêdo et al, 2009;Skala, 2010;Cuomo et al, 2017).…”

Three-Dimensional Velocity Field Interpolation Based on Attention Mechanism

“…Under such circumstances, introducing deep learning methods brings new possibilities for 3D interpolation. The application of three-dimensional interpolation technology is also used in medical imaging [9][10][11][12][13][14], hydrological analysis [15], atmospheric sciences [16], hydrodynamics [17], virtual reality [18], and other fields. Mikhailiuk A et al [19] first achieved the restoration of the full picture of seismic data from 20% of actual data through a deep autoencoder.…”