Three-dimensional Interpolation Method Research Articles

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

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.

Tridimensional spatial distribution of manganese in a river impacted by metallurgical activity and mining.

A three-dimensional interpolation method based on a digital elevation model (DEM) was developed to assess the impact of mining and metallurgical activity on the Claro River (Hidalgo, Mexico). This method was used to analyze the spatial concentration of manganese in sediments, water, and fish (viscera and muscle). Input data correspond to chemical manganese (Mn) analysis of the aforementioned environmental matrices, mining discharge volumes, and rainfall data. The three-dimensional model made it possible to (a) define Mn dispersion (19 km for sediments and 13 km for viscera); (b) identify northern meanders of the Claro River as areas of Mn accumulation in sediments and fish; and (c) determine river features that influence Mn concentration in fish. Results indicate that Mn concentration increases in areas receiving industrial discharges, as well as in meanders located near Acuimantla village. Total Mn levels in the water are between < 0.01 and 6.57 mg/L, while soluble and colloidal Mn concentrations range from < 0.01 to 0.49 mg/L. The highest Mn values in the water (total Mn: 6.57 mg/L and soluble-colloidal Mn: 0.49 mg/L) were detected in tributary rivers near industrial discharge sites. The concentration in water compared with that in sediments (160-213,867 mg/kg) and fish (viscera: 5-5236 mg/kg and muscle: 10.7-398.8 mg/kg) indicates low solubility of this mineral. The geoaccumulation index (Igeo) and contamination factor (CF) show that sediment composition has been affected.

Numerical integration to obtain moment of inertia of nonhomogeneous material

The moment of inertia of a continuous object with an arbitrary shape made of a nonhomogeneous material is usually calculated by dividing it into small domains. However, it is a burdensome process to specify the density of the small domains. When the Monte Carlo method is used in the case of an arbitrary shape, the computation time increases. In this paper, a technique of easily calculating the moment of inertia of a 3D nonhomogeneous material using boundary integral equations is proposed. It is also shown how to calculate the mass, primary moment, and center of mass of an arbitrary object made of a nonhomogeneous material. A technique employed in the triple-reciprocity boundary element method is used to evaluate integral. In this paper, a formulization of the boundary element method is utilized, and a technique for the direct numerical integration of the three-dimensional domain using a three-dimensional interpolation method without carrying out domain division is proposed. To investigate the efficiency of this technique, several numerical examples are given.

Interpolación tridimensional en campos escalares

Se presenta en detalle el desarrollo de la interpolación tridimensional para campos escalares, que consiste en generar información en cualquier punto del espacio, sobre alguna variable dependiente de las tres coordenadas cartesianas, en algún volumen definido. Esto a partir de un conjunto discreto de datos que representan el valor de la variable dependiente en puntos específicos del espacio.&lt;br /&gt;Se desarrolla un método de interpolación tridimensional basado en obtener las coordenadas de todos los vecinos del punto de interés. Para luego asignar un peso relativo a cada uno de estos puntos, en función de la proximidad con el lugar donde se busca un nuevo valor de la variable dependiente. Este procedimiento se presenta en forma de diagrama de flujo, para que pueda ser desarrollado en cualquier lenguaje de programación.&lt;br /&gt;El método propuesto es implementado en un código en software comercial y a la vez es validado al confrontar sus resultados con los que genera una función propia del software Matlab. Dicha función es detallada a profundidad para facilitar a cualquier usuario su utilización, estableciendo además las limitaciones y diferencias entre el uso de esta función y la implementación del método propuesto en un código computacional.&lt;br /&gt;Se encuentra que el método propuesto es altamente confiable y que a su vez permite, eventualmente, adaptarse a condiciones donde la distribución de información en el espacio sea irregular o no se disponga de algún dato dentro de una matriz estructurada de mediciones.

Application of Three-Dimensional Interpolation Methods in Contaminated Site Evaluation

Contaminated sites remediation is one of the hot points in environmental protection fields. Therefore, an important research project is how to expediently determine the bound and level of pollution of contaminated sites. This may help to decide on a timely and accurate rescue plan so as to minimize the costs and to improve the effect of restoration. This is also the basis of contaminated sites remediation acceptance. There are many influencing factors to confirm the remediation areas on contaminated sites. Studies show that three-dimensional interpolation method is effective tool to delimit the pollution scope. Different three-dimensional interpolation methods have different results in contaminate distribution prediction and directly affect the boundary of contamination. This paper selects one specific case with heavy metal lead contamination to study three-dimensional interpolation methods. The three-dimensional stratigraphic model is established for uncertainty analysis and error analysis in the grid through KrigingIDW(Shepard) and nearest neighbor interpolation method. Results show that 40m*40m grids have the highest accuracy of stratigraphic simulation. Nearest neighbor interpolation method is most suitable for stratigraphic model building. Kriging interpolation method is more suitable for constructing three-dimensional pollutant prediction model. On the basis of above, this text established one distribution prediction model of soil lead contamination, and calculated the contaminated earthwork quantity under different remediation goals. Finally, the paper achieved three-dimensional visualization of the site soil contamination. This study can be directly applied to the actual site remediation decision process, and is helpful for the contaminated sites evaluation and restoration in the future.

Numerical Integration for Three-Dimensional Meshless BEM

The conventional boundary element method (BEM) uses internal cells for the domain integrals when solving nonlinear problems or problems with domain effects. In the conventional BEM, however, the merit of the BEM, which is easy preparation of data, is lost. This paper presents numerical integration for a three-dimensional meshless BEM, which does not require the use of internal cells. This method uses arbitrary internal points instead of internal cells. In this paper, a three-dimensional interpolation method is proposed. Furthermore, three-dimensional numerical integration is proposed using the above-mentioned three-dimensional interpolation method. This method is based on an improved multiple-reciprocity BEM (triple-reciprocity BEM) for heat conduction analysis with heat generation. In order to investigate the efficiency of this method, several numerical examples are given.

Experimental verification study for system for prediction of environmental emergency dose information; SPEEDI. (I). Three-dimensional interpolation method for surface wind observations in complex terrain to produce gridded wind field.

In order to calculate airflow around a nuclear site, a new weighted interpolation method for sparse wind data at various terrain heights is developed. This method employs weighting functions for vertical distance and the topographic barrier between the station and a grid point, in addition to a weighting function for horizontal distance which is employed in usual methods. The new weighting functions are developed from the analysis of field measurements taken in complex terrain. This method can represent the wind-fields from the bottom to the upper boundary better than usual methods which use only the horizontal weighting factor, even when the upper wind data are not available.