A new strategy for the atmospheric gravity effect in gravimetric geoid determination

Prior to Stokes integration, the gravitational effect of atmospheric masses must be removed from the gravity anomaly g. One theory for the atmospheric gravity effect on the geoid is the well-known International Association of Geodesy approach in connection with Stokes integral formula. Another strategy is the use of a spherical harmonic representation of the topography, i.e. the use of a global topography computed from a set of spherical harmonics. The latter strategy is improved to account for local information. A new formula is derived by combining the local contribution of the atmospheric effect computed from a detailed digital terrain model and the global contribution computed from a spherical harmonic model of the topography. The new formula is tested over Iran and the results are compared with corresponding results from the old formula which only uses the global information. The results show significant differences. The differences between the two formulas reach 17 cm in a test area in Iran.     

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

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.     

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

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.     

Spherical particles as tracers of atmospheric ceramic industry

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.     

Wavelet Modeling of Regional and Temporal Variations of the Earth’s Gravitational Potential Observed by GRACE

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     

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

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.     

A reduced grid for a parallel global ocean general circulation model

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.     

青藏高原东缘中南部主要活动断裂滑动速率及其地震矩亏损

作为青藏高原南东向“挤出逃逸”的重要通道,青藏高原东缘中南部具有大型走滑断裂广泛发育和地震活动强烈而频繁的特征.本文使用线性球面块体模型理论,在前人活动地块研究的基础上吸收新近研究成果,建立研究区三维块体几何模型,使用1999—2007年的GPS数据反演得到青藏高原东缘中南部主要活动断裂滑动速率.使用反演得到的滑动速率和最优断层闭锁深度估算了川滇菱形块体主要边界和其内部断裂的地震矩积累,并利用历史强震目录估算了地震矩释放,在比较两者差异的基础上得到了研究区地震矩亏损（未释放的地震矩）较大的断层和断层段,该结果可以作为研究区强震中长期危险性研究的参考.     

基于非均一场源的球坐标大地电磁模拟方法

大地电磁测深理论与数据处理解释均假定平面电磁波垂直入射地下空间,但随着研究尺度的逐渐扩大,使得因地球弧度产生的影响难以忽略.此时,传统笛卡尔坐标体系及平面波场源不再适用于大尺度的大地电磁数据正反演解释.本文提出并实现了一种基于球坐标系的大地电磁交错网格有限差分三维正演算法,并对电场进行极向-环向分解,结合球谐函数和贝塞尔函数构建了可取代平面波的场源模型.首先利用经纬度信息构建三维地电模型,将场源设置于模型空间正上方,然后通过直接求解球坐标系下麦克斯韦方程来获得大地电磁响应.在此基础上,本文设计了球坐标下具有不同分辨率的多个三维地电模型,阐述了由球体模型到笛卡尔模型的转换方法,详细对比了两种坐标体系在计算效率、所求得的电场和视电阻率方面的差异.结果表明二者差异度主要与电性横向分布和地图投影方法有关,与周期并不存在明显的单调递增关系.