An Eulerian flux-form advection scheme, called the Two-step Shape-Preserving Advection Scheme （TSPAS）, was generalized and implemented on a spherical icosahedral hexagonal grid （also referred to as a geodesic grid...An Eulerian flux-form advection scheme, called the Two-step Shape-Preserving Advection Scheme （TSPAS）, was generalized and implemented on a spherical icosahedral hexagonal grid （also referred to as a geodesic grid） to solve the transport equation. The C grid discretization was used for the spatial discretization. To implement TSPAS on an unstructured grid, the original finite-difference scheme was further generalized. The two-step integration utilizes a combination of two separate schemes （a low-order monotone scheme and a high-order scheme that typically cannot ensure monotonicity） to calculate the fluxes at the cell walls （one scheme corresponds to one cell wall）. The choice between these two schemes for each edge depends on a pre-updated scalar value using slightly increased fluxes. After the determination of an appropriate scheme, the final integration at a target cell is achieved by summing the fluxes that are computed by the different schemes. The conservative and shape-preserving properties of the generalized scheme are demonstrated. Numerical experiments are conducted at several horizontal resolutions. TSPAS is compared with the Flux Corrected Transport （FCT） approach to demonstrate the differences between the two methods, and several transport tests are performed to examine the accuracy, efficiency and robustness of the two schemes.展开更多
【目的】全球离散格网系统(Discrete Global Grid Systems,DGGS)本质上是多尺度栅格结构,地理空间矢量与格网的集成是难点,矢量线格网化是其中的基本问题。现有方案多以平面格网单元中心(格心)连线为矢量线建模结果,但扩展到球面后建模...【目的】全球离散格网系统(Discrete Global Grid Systems,DGGS)本质上是多尺度栅格结构,地理空间矢量与格网的集成是难点,矢量线格网化是其中的基本问题。现有方案多以平面格网单元中心(格心)连线为矢量线建模结果,但扩展到球面后建模精度降低,本文针对这一缺陷提出矢量线全球离散格网系统高精度建模方法。【方法】首先选择与地球拟合程度更高的菱形三十面体构建六边形格网系统,以3个相邻菱形面构成组合结构并建立三轴整数坐标系描述单元空间位置;然后根据矢量线首尾端点所在单元确定最优方向编码以减少搜索范围,通过编码邻近运算搜索矢量线经过的球面单元,以球面格心连线为建模结果并提出跨面矢量线处理方法;最后增加单元顶点(格点)作为结构要素,实现多结构要素矢量线建模,进一步提高建模精度。【结果】实验结果表明:本文方案能正确实现全球各个大洲海岸线格网化建模,确保格网化单元与矢量线拓扑相交,且相较平面格网建模结果兼具精度和效率优势。【结论】针对传统矢量数据格网建模方法的几何精度损失和拓扑畸变问题,本文提出高精度球面格网化建模方法,为矢量数据转换至格网同构处理提供有力支撑。展开更多
Discrete Global Grid Systems(DGGSs) are spatial references that use a hierarchical tessellation of cells to partition and address the entire globe. They provide an organizational structure that permits fast integratio...Discrete Global Grid Systems(DGGSs) are spatial references that use a hierarchical tessellation of cells to partition and address the entire globe. They provide an organizational structure that permits fast integration between multiple sources of large and variable geospatial data sufficient for visualization and analysis. Despite a significant body of research supporting hexagonal DGGSs as the superior choice, the application thereof has been hindered owing in part to the lack of a rational hierarchy with an efficient addressing system. This paper presents an algebraic model of encoding scheme for the Aperture 3 Hexagonal(A3H) DGGS. Firstly, the definition of a grid cell, which is composed of vertices, edges, and a center, is introduced to describe fundamental elements of grids. Secondly, by identifying the grid cell with its center, this paper proves that cell centers at different levels can be represented exactly using a mixed positional number system in the complex plane through the recursive geometric relationship between two successive levels, which reveals that grid cells are essentially special complex radix numbers. Thirdly, it is shown that through the recursive geometric relationship of successive odd or even levels, the mixed positional number system can also be applied to uniquely represent cell centers at different levels under specific constraint conditions, according to which the encoding scheme is designed. Finally, it is shown that by extending the scheme to 20 triangular faces of the regular icosahedron,multi-resolution grids on closed surfaces of the icosahedron are addressed perfectly. Contrast experiments show that the proposed encoding scheme has the advantages of theoretical rigor and high programming efficiency and that the efficiency of cross-face adjacent cell searching is 242.9 times that of a similar scheme. Moreover, the proposed complex radix number representation is an ideal formalized description tool for grid systems. The research ideas introduced herein can be used to create a universal theoretical framework for DGGSs.展开更多
Global ocean surface currents estimated from satellite derived data based on a regular global grid are affected by the grid’s shape and placement.Due to different neighbourhood relationships,the rectangular lat/lon g...Global ocean surface currents estimated from satellite derived data based on a regular global grid are affected by the grid’s shape and placement.Due to different neighbourhood relationships,the rectangular lat/lon grids lose accuracy when interpolating andfitting elevation data.Hexagonal grids have shown to be advantageous due to their isotropic,uniform neighbourhood.Considering these merits,this paper aims to estimate global ocean surface current using a global isotropic hexagonal grid from satellite remote sensing data.First,gridded satellite altimeter data and wind data with different resolutions are interpolated into the centre of the global isotropic hexagonal grid.Then,geostrophic and Ekman currents components are estimated according to the Lagerlof Ocean currents theory.Finally,the inversion results are verified.By analyzing the results,we conclude that the ocean surface currents estimated based on the global isotropic hexagonal grid have considerable accuracy,with improvement over rectangular lat/lon grids.展开更多
Although research on the discrete global grid systems (DGGSs) has become an essential issue in the era of big earth data,there is still a gap between the efficiency of current encoding and operation schemes for hexago...Although research on the discrete global grid systems (DGGSs) has become an essential issue in the era of big earth data,there is still a gap between the efficiency of current encoding and operation schemes for hexagonal DGGSs and the needs of practical applications. This paper proposes a novel and efficient encoding and operation scheme of an optimized hexagonal quadtree structure (OHQS) based on aperture 4 hexagonal discrete global grid systems by translation transformation. A vector model is established to describe and calculate the aperture 4 hexagonal grid system. This paper also provides two different grid code addition algorithms based on induction and ijk coordinate transformation. We implement the transformation between OHQS codes and geographic coordinates through the ij,ijk and IJK coordinate systems. Compared with existing schemes,the scheme in this paper greatly improves the efficiency of the addition operation,neighborhood retrieval and coordinate transformation,and the coding is more concise than other aperture 4 hexagonal DGGSs. The encoding operation based on the ijk coordinate system is faster than the encoding operation based on the induction and addition table. Spatial modeling based OHQS DGGSs are also provided. A case study with rainstorms demonstrated the availability of this scheme.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.41505066)the Basic Scientific Research and Operation Foundation of Chinese Academy Meteorological Sciences(Grant Nos.2015Z002,2015Y005)the National Research and Development Key Program:Global Change and Mitigation Strategies(No.2016YFA0602101)
文摘An Eulerian flux-form advection scheme, called the Two-step Shape-Preserving Advection Scheme （TSPAS）, was generalized and implemented on a spherical icosahedral hexagonal grid （also referred to as a geodesic grid） to solve the transport equation. The C grid discretization was used for the spatial discretization. To implement TSPAS on an unstructured grid, the original finite-difference scheme was further generalized. The two-step integration utilizes a combination of two separate schemes （a low-order monotone scheme and a high-order scheme that typically cannot ensure monotonicity） to calculate the fluxes at the cell walls （one scheme corresponds to one cell wall）. The choice between these two schemes for each edge depends on a pre-updated scalar value using slightly increased fluxes. After the determination of an appropriate scheme, the final integration at a target cell is achieved by summing the fluxes that are computed by the different schemes. The conservative and shape-preserving properties of the generalized scheme are demonstrated. Numerical experiments are conducted at several horizontal resolutions. TSPAS is compared with the Flux Corrected Transport （FCT） approach to demonstrate the differences between the two methods, and several transport tests are performed to examine the accuracy, efficiency and robustness of the two schemes.
文摘【目的】全球离散格网系统(Discrete Global Grid Systems,DGGS)本质上是多尺度栅格结构,地理空间矢量与格网的集成是难点,矢量线格网化是其中的基本问题。现有方案多以平面格网单元中心(格心)连线为矢量线建模结果,但扩展到球面后建模精度降低,本文针对这一缺陷提出矢量线全球离散格网系统高精度建模方法。【方法】首先选择与地球拟合程度更高的菱形三十面体构建六边形格网系统,以3个相邻菱形面构成组合结构并建立三轴整数坐标系描述单元空间位置;然后根据矢量线首尾端点所在单元确定最优方向编码以减少搜索范围,通过编码邻近运算搜索矢量线经过的球面单元,以球面格心连线为建模结果并提出跨面矢量线处理方法;最后增加单元顶点(格点)作为结构要素,实现多结构要素矢量线建模,进一步提高建模精度。【结果】实验结果表明:本文方案能正确实现全球各个大洲海岸线格网化建模,确保格网化单元与矢量线拓扑相交,且相较平面格网建模结果兼具精度和效率优势。【结论】针对传统矢量数据格网建模方法的几何精度损失和拓扑畸变问题,本文提出高精度球面格网化建模方法,为矢量数据转换至格网同构处理提供有力支撑。
基金supported by the National Natural Science Foundation of China (Grant No. 41671410)the Postdoctoral Science Foundation of China (Grant No. 2013T60161)the Excellent Young Scholar Foundation of Information Engineering University (Grant No. 2016610802)
文摘Discrete Global Grid Systems(DGGSs) are spatial references that use a hierarchical tessellation of cells to partition and address the entire globe. They provide an organizational structure that permits fast integration between multiple sources of large and variable geospatial data sufficient for visualization and analysis. Despite a significant body of research supporting hexagonal DGGSs as the superior choice, the application thereof has been hindered owing in part to the lack of a rational hierarchy with an efficient addressing system. This paper presents an algebraic model of encoding scheme for the Aperture 3 Hexagonal(A3H) DGGS. Firstly, the definition of a grid cell, which is composed of vertices, edges, and a center, is introduced to describe fundamental elements of grids. Secondly, by identifying the grid cell with its center, this paper proves that cell centers at different levels can be represented exactly using a mixed positional number system in the complex plane through the recursive geometric relationship between two successive levels, which reveals that grid cells are essentially special complex radix numbers. Thirdly, it is shown that through the recursive geometric relationship of successive odd or even levels, the mixed positional number system can also be applied to uniquely represent cell centers at different levels under specific constraint conditions, according to which the encoding scheme is designed. Finally, it is shown that by extending the scheme to 20 triangular faces of the regular icosahedron,multi-resolution grids on closed surfaces of the icosahedron are addressed perfectly. Contrast experiments show that the proposed encoding scheme has the advantages of theoretical rigor and high programming efficiency and that the efficiency of cross-face adjacent cell searching is 242.9 times that of a similar scheme. Moreover, the proposed complex radix number representation is an ideal formalized description tool for grid systems. The research ideas introduced herein can be used to create a universal theoretical framework for DGGSs.
文摘Global ocean surface currents estimated from satellite derived data based on a regular global grid are affected by the grid’s shape and placement.Due to different neighbourhood relationships,the rectangular lat/lon grids lose accuracy when interpolating andfitting elevation data.Hexagonal grids have shown to be advantageous due to their isotropic,uniform neighbourhood.Considering these merits,this paper aims to estimate global ocean surface current using a global isotropic hexagonal grid from satellite remote sensing data.First,gridded satellite altimeter data and wind data with different resolutions are interpolated into the centre of the global isotropic hexagonal grid.Then,geostrophic and Ekman currents components are estimated according to the Lagerlof Ocean currents theory.Finally,the inversion results are verified.By analyzing the results,we conclude that the ocean surface currents estimated based on the global isotropic hexagonal grid have considerable accuracy,with improvement over rectangular lat/lon grids.
基金supported by the Strategic Priority Research Program of Chinese Academy of Sciences [grant number XDA19020201].
文摘Although research on the discrete global grid systems (DGGSs) has become an essential issue in the era of big earth data,there is still a gap between the efficiency of current encoding and operation schemes for hexagonal DGGSs and the needs of practical applications. This paper proposes a novel and efficient encoding and operation scheme of an optimized hexagonal quadtree structure (OHQS) based on aperture 4 hexagonal discrete global grid systems by translation transformation. A vector model is established to describe and calculate the aperture 4 hexagonal grid system. This paper also provides two different grid code addition algorithms based on induction and ijk coordinate transformation. We implement the transformation between OHQS codes and geographic coordinates through the ij,ijk and IJK coordinate systems. Compared with existing schemes,the scheme in this paper greatly improves the efficiency of the addition operation,neighborhood retrieval and coordinate transformation,and the coding is more concise than other aperture 4 hexagonal DGGSs. The encoding operation based on the ijk coordinate system is faster than the encoding operation based on the induction and addition table. Spatial modeling based OHQS DGGSs are also provided. A case study with rainstorms demonstrated the availability of this scheme.
