On the estimation of a multi-resolution representation of the gravity field based on spherical harmonics and wavelets     

M. Schmidt  O. Fabert  C.K. Shum 《Journal of Geodynamics》2005,39(5):512

The gravitational potential of the Earth is usually modeled by means of a series expansion in terms of spherical harmonics. However, the computation of the series coefficients requires preferably homogeneous distributed global data sets. Since one of the most important features of wavelet functions is the ability to localize both in the spatial and in the frequency domain, regional and local structures may be modeled by means of a spherical wavelet expansion. In general, applying wavelet theory a given input data set is decomposed into a certain number of frequency-dependent detail signals, which can be interpreted as the building blocks of a multi-resolution representation. On the other hand, there is no doubt that the low-frequency part of the geopotential can be modeled appropriately by means of spherical harmonics. Hence, the main idea of this paper is to derive a combined model consisting of an expansion in spherical harmonics for the low-frequency part and an expansion in spherical wavelets for the remaining medium and high-frequency parts of the gravity field. Furthermore, an appropriate parameter estimation procedure is outlined to solve for the unknown model coefficients.  相似文献   

A unified formulation for the three-dimensional shallow water equations using orthogonal co-ordinates: theory and application     

Herman W. J. Kernkamp  Henri A. H. Petit  Herman Gerritsen  Erik D. de Goede 《Ocean Dynamics》2005,55(3-4):351-369

In this paper, the formulations of the primitive equations for shallow water flow in various horizontal co-ordinate systems and the associated finite difference grid options used in shallow water flow modelling are reviewed. It is observed that horizontal co-ordinate transformations do not affect the chosen co-ordinate system and representation in the vertical, and are the same for the three- and two-dimensional cases. A systematic derivation of the equations in tensor notation is presented, resulting in a unified formulation for the shallow water equations that covers all orthogonal horizontal grid types of practical interest. This includes spherical curvilinear orthogonal co-ordinate systems on the globe. Computational efficiency can be achieved in a single computer code. Furthermore, a single numerical algorithmic code implementation satisfies. All co-ordinate system specific metrics are determined as part of a computer-aided model grid design, which supports all four orthogonal grid types. Existing intuitive grid design and visual interpretation is conserved by appropriate conformal mappings, which conserve spherical orthogonality in planar representation. A spherical curvilinear co-ordinate solution of wind driven steady channel flow applying a strongly distorted grid is shown to give good agreement with a regular spherical co-ordinate model approach and the solution based on a β-plane approximation. Especially designed spherical curvilinear boundary fitted model grids are shown for typhoon surge propagation in the South China Sea and for ocean-driven flows through Malacca Straits. By using spherical curvilinear grids the number of grid points in these single model grid applications is reduced by a factor of 50–100 in comparison with regular spherical grids that have the same horizontal resolution in the area of interest. The spherical curvilinear approach combines the advantages of the various grid approaches, while the overall computational effort remains acceptable for very large model domains.  相似文献   

Spherical particles as tracers of atmospheric ceramic industry     

M. M. Jordán  C. Álvarez  T. Sanfeliu 《Environmental Geology》2006,51(3):447-453

Castellón province houses the nucleus of ceramics production in Spain (93%). This nucleus, located around in the villages of Castellón, Villarreal, Alcora and Onda, has gone through a special process of industrial expansion. The emissions, most of them of particulate material, can constitute a real environmental problem. A study designed to identify the crystalline and glassy phases in the depositable particulate material has been carried out by SEM/EDX and X-ray diffraction methods. Quartz, calcite, illite, kaolinite, chlorite, and feldspars have been the main crystalline phases identified. The number of spherical morphology particles found in the depositable material is remarkable. The vitreous material found was spherical nodules. Due to the shape, size (1–10 μm), and chemical composition of these particles, they can be excellent tracers of the ceramics industry emissions.The presence of Zn, Ba, or Fe are due to the massive use of these substances as opacifying and pigmentation agents in many ceramics frits and glaze compositions. This fact gives a valuable information that will facilitate the studies guided to obtain important aims such as: toxicology, average size of a particle, formation mechanisms, etc.  相似文献   

Wavelet Modeling of Regional and Temporal Variations of the Earth’s Gravitational Potential Observed by GRACE   总被引：1，自引：0，他引：1  

M. J. Fengler  W. Freeden  A. Kohlhaas  V. Michel  T. Peters 《Journal of Geodesy》2007,81(1):5-15

This work is dedicated to the wavelet modeling of regional and temporal variations of the Earth’s gravitational potential observed by the GRACE (gravity recovery and climate experiment) satellite mission. In the first part, all required mathematical tools and methods involving spherical wavelets are provided. Then, we apply our method to monthly GRACE gravity fields. A strong seasonal signal can be identified which is restricted to areas where large-scale redistributions of continental water mass are expected. This assumption is analyzed and verified by comparing the time-series of regionally obtained wavelet coefficients of the gravitational signal originating from hydrology models and the gravitational potential observed by GRACE. The results are in good agreement with previous studies and illustrate that wavelets are an appropriate tool to investigate regional effects in the Earth’s gravitational field. Electronic Supplementary Material Supplementary material is available for this article at  相似文献   

虚拟球谐方法逼近市级大地水准面计算分析     

王建强  孙云龙 《大地测量与地球动力学》2022,42(2):115-118

研究了构建市级大地水准面的虚拟球谐方法。首先,选择构建区域的中心点和区域半径对观测值进行数据预处理,并统计分析数值范围和位置信息;然后,将观测值由地理坐标系转换到球冠坐标系,再转换到虚拟球坐标系中;最后,根据虚拟球谐方法构建市级大地水准面。以南昌市为例构建采样点,采用多项式拟合和神经网络方法与本文虚拟球谐方法进行比较分析,结果表明,虚拟球谐方法的RMS值为0.308 cm,拟合效果最好。  相似文献   

Flow of grounded abyssal ocean currents along zonally-varying topography on a rotating sphere     

Gordon E. Swaters 《地球物理与天体物理流体动力学》2013,107(5):564-586

A steady nonlinear planetary–geostrophic model in spherical coordinates is presented describing the hemispheric-scale meridional flow of grounded abyssal currents on a zonally-sloping bottom. The model, which corresponds mathematically to a quasi-linear hyperbolic partial differential equation, can be solved explicitly for a cross-slope isopycnal field that is grounded (i.e. intersects the bottom on the up slope and down slope sides). As a consequence of the conservation of potential vorticity, the abyssal currents possess decreasing thickness in the equatorward direction while maintaining constant meridional volume transport. There is a small westward zonal transport in the interior of these currents that results in westward intensification as they flow toward the equator. Conditions for the possible formation of a shock to develop on the up slope flank of the current are derived.  相似文献   

Vector and scalar spherical harmonic spectral equations for rapidly rotating anisotropic alpha-effect dynamos     

C. G. Phillips 《地球物理与天体物理流体动力学》2013,107(6):640-666

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Effects on the nutation of C4,m and S4,m Harmonics     

marta Folgueira  Jean Souchay  Hiroshi Kinoshita 《Celestial Mechanics and Dynamical Astronomy》1998,70(3):147-157

In this paper, we make a study about the influence of the coefficients of the geopotential C_4,m and S_4,m, (m=1,2,3,4) on the nutation, starting from the Hamiltonian theory as developed by Kinoshita (1977).We obtain ten coefficients larger than 0.05 μ as for the nutation in longitude and six for the nutation in obliquity. The present results are included in the reconstruction of the theory of nutation (REN‐2000) at the level of truncation of 0.1 μ as (Souchay et al., 1997). This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

A reduced grid for a parallel global ocean general circulation model     

M. E. Wickett  P. B. Duffy  G. Rodrigue 《Ocean Modelling》2000,2(3-4)

A limitation of many global climate models with explicit finite-difference numerics is the timestep restriction caused by the decrease in cell size associated with the convergence of meridians near the poles. To keep the longitudinal width of model cells as uniform as possible, we apply a “reduced” grid to a three-dimensional primitive equation ocean-climate model. With this grid the number of cells in the longitudinal direction is reduced at high latitudes. The grid consists of subgrids which interact at interfaces along their northern and southern boundaries, where the resolution changes by a factor of three. We extend the finite-difference techniques to these interfaces, focusing on the conservation required to perform long time integrations, while preserving the staggered spatial arrangement of variables and the numerics used on subgrids. The common alternative used to reduce the timestep restriction caused by the spherical grid is the filtering of high-frequency modes from the high-latitude solution. The reduced grid allows an increased timestep while eliminating the need for filtering and reduces execution time per model step by roughly 20%. We implement the reduced grid model for parallel computer architectures with two-dimensional domain decomposition and message passing, with speedup results similar to those of the original model. We present results of model runs showing small effects on the solution and sizable improvements to the execution time.  相似文献