On the existence of atmospheric attractors

In this paper, we consider the long-time dynamics for the primitive equations of large-scale dry at- mosphere. First, by energy methods, we obtain the existence and uniqueness of global strong solu- tions of the problem. Second, by studying the long-time behavior of strong solutions, we construct a global attractor which captures all the trajectories.     

Existence of the atmosphere attractor

The global asymptotic behavior of solutions for the equations of large scale atmospheric motion with the non-stationary external forcing is studied in the infinite dimensional Hilbert space. Based on the properties of operators of the equations, some energy inequalities and the uniqueness theorem of solutions are obtained. On the assumption that external forces are bounded, the exsitence of the global absorbing set and the atmosphere attractor is proved, and the characteristics of the decay of effect of initial field and the adjustment to the external forcing are revealed. The physical sense of the results is discussed and some ideas about climatic numerical forecast are elucidated Work supported by the State Key Research Project on Dynamics and Predictive Theory of the Climate.     

半拉格朗日模式风的半解析解及与差分解的比较试验

质点的轨迹计算是半拉格朗日模式的重要基础,传统的数值计算方法由于采用时间差分代替微分,只能得到质点运动轨迹终点的速度,因此质点的移动轨迹（位移）只能靠风速外推的方法计算,导致了模式计算不稳定等问题.借鉴精细积分法中使用半解析解的思路,利用正压原始方程研究了用运动方程的半解析解构建数值模式的可能性.求解了运动方程的一阶和二阶微分方程组的半解析解,通过时间积分半解析解计算质点运动轨迹.数值试验表明,一阶微分方程组的半解析解比差分解略有优势.二阶微分方程组的半解析解在时间步长增大时优势非常明显,而且在保证计算精度的前提下,节省计算时间,这对提高模式性能有重要作用.     

Balancing the source terms in a SPH model for solving the shallow water equations

A shallow flow generally features complex hydrodynamics induced by complicated domain topography and geometry. A numerical scheme with well-balanced flux and source term gradients is therefore essential before a shallow flow model can be applied to simulate real-world problems. The issue of source term balancing has been exhaustively investigated in grid-based numerical approaches, e.g. discontinuous Galerkin finite element methods and finite volume Godunov-type methods. In recent years, a relatively new computational method, smooth particle hydrodynamics (SPH), has started to gain popularity in solving the shallow water equations (SWEs). However, the well-balanced problem has not been fully investigated and resolved in the context of SPH. This work aims to discuss the well-balanced problem caused by a standard SPH discretization to the SWEs with slope source terms and derive a corrected SPH algorithm that is able to preserve the solution of lake at rest. In order to enhance the shock capturing capability of the resulting SPH model, the Monotone Upwind-centered Scheme for Conservation Laws (MUSCL) is also explored and applied to enable Riemann solver based artificial viscosity. The new SPH model is validated against several idealized benchmark tests and a real-world dam-break case and promising results are obtained.     

Development and deployment of an instrument for measurement of atmospheric peroxy radical by chemical amplification

An instrument for measurement of peroxy radical by chemical amplification (PERCA) has been devel- oped at Peking University (PKU) and deployed in several field campaigns. PKU PERCA measures per- oxy radical via amplification of NO2 by peroxy radical in the presence of NO and CO through a chain reaction. The amount of amplified NO2 is detected by a NO2-luminal chemiluminescence detector. The chain length (CL) of 75±20 (1σ ) was determined routinely during field campaigns using a HO2 source from photolysis of...     

A class of analytic solutions of the magnetic force-free field equations

Abstract

Formation of electric current sheets in the corona is thought to play an important role in solar flares, prominences and coronal heating. It is therefore of great interest to identify magnetic field geometries whose evolution leads to variations in B over small length-scales. This paper considers a uniform field B ₀[zcirc], line-tied to rigid plates z = ±l, which are then subject to in-plane displacements modeling the effect of photospheric motion. The force-free field equations are formulated in terms of field-line displacements, and when the imposed plate motion is a linear function of position, these reduce to a 4 × 4 system of nonlinear, second-order ordinary differential equations. Simple analytic solutions are derived for the cases of plate rotation and shear, which both tend to form singularities in certain parameter limits. In the case of plate shear there are two solution branches—a simple example of non-uniqueness.     

基于Zoeppritz偏导方程精确解的地层密度多角度反演

基于Zoeppritz方程对介质密度偏导数所建立的偏导方程的精确解,构造了多角度反演地层介质密度的反演方程,在偏导数求解过程中考虑了介质密度对波速度的影响因素,并由此实现了利用反射系数梯度精确解计算地层密度的多角度联合反演.通过数值算例考察了计算方法,结果显示:反演方法对层状地层模型不论反射波是否存在相干现象均获得了较好的反演结果,反演迭代10次后计算结果的最大相对误差能够收敛到1%之内;随着反演角度的增加地层介质密度反演的精度逐步提高,反演具有自动校正能力,有快的计算速度.本方法克服了传统AVO(Amplitude Versus Offset)基于Zoeppritz方程近似所遇到的困难,不受反演角度大小及反射界面对波反射强弱的限制,为地层介质密度的多角度包括大角度反演提供了一种新的快速有效的计算方法.     

强震前震中区域的临震气象和近地表大气静电特征

通过对200多例国内外强震前7小时震中区域气象条件的分析,发现强震发生前均为晴天天气.据此选择晴天气象条件下发生的100多例3—8级国内外地震,分析大气静电场观测信号特征,发现震中及附近区域在震前约3—24小时的临震时段内,具有近地表静电场异常反向现象.文中用于研究的晴天气象条件标准是:①水汽少,即相对湿度要低(排除降...     

The quasi－static solutions of two kinds of the thermo－elastic problem and the time spacedistributionfeatureoftheseismicprecursorfields

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On the Mathematical Analysis of an Elastic-gravitational Layered Earth Model for Magmatic Intrusion: The Stationary Case

In the early eighties Rundle (1980, 1981a,b, 1982) developed the techniques needed for calculations of displacements and gravity changes due to internal sources of strain in layered linear elastic-gravitational media. The approximation of the solution for the half space was obtained by using the propagator matrix technique. The Earth model considered is elastic-gravitational, composed of several homogeneous layers overlying a bottom half space. Two dislocation sources can be considered, representing magma intrusions and faults. In recent decades theoretical and computational extensions of that model have been developed by Rundle and co-workers (e.g., Fernández and Rundle, 1994a,b; Fernández et al., 1997, 2005a; Tiampo et al., 2004; Charco et al., 2006, 2007a,b). The source can be located at any depth in the media. In this work we prove that the perturbed equations representing the elastic-gravitational deformation problem, with the natural boundary and transmission conditions, leads to a well-posed problem even for varied domains and general data. We present constructive proof of the existence and we show the uniqueness and the continuous dependence with respect to the data of weak solutions of the coupled elastic-gravitational field equations.     

地震波的场方程矩阵和能量的正定二次型及其意义

场方程是能够表述半空间地震波场的整体特征.波动方程、速度方程和能量方程.通过分析可知每个场方程都具有各自的“场方程矩阵”.能量方程能够对所有场方程矩阵进行综合和贯通,给出了能量方程以“弹性矩阵”为核心的普适性表达形式.最后,运用矩阵的正定二次型理论阐述了“能量矩阵与弹性矩阵”之间一致的对称性和正定性.能量矩阵蕴含的动态力的平衡关系、速度的时间_空间分布和能量的传播及变化的物理意义,能够从能量矩阵的正定二次型特性表述出来.本文研究分析问题的方法完全适用于复杂介质模型,相关的认识和结论可以拓展到均匀黏弹性各向同性介质、均匀弹性各向异性介质、均匀黏弹性各向异性介质以及比奥饱和流体介质.     

Three-dimensional solutions of the magnetohydrostatic equations for rigidly rotating magnetospheres in cylindrical coordinates

We present new analytical three-dimensional solutions of the magnetohydrostatic equations, which are applicable to the co-rotating frame of reference outside a rigidly rotating cylindrical body, and have potential applications to planetary magnetospheres and stellar coronae. We consider the case with centrifugal force only, and use a transformation method in which the governing equation for the “pseudo-potential” (from which the magnetic field can be calculated) becomes the Laplace partial differential equation. The new solutions extend the set of previously found solutions to those of a “fractional multipole” nature, and offer wider possibilities for modelling than before. We consider some special cases, and present example solutions.     

亚热带地区典型水库流域氮、磷湿沉降及入湖贡献率估算

为了探究汤浦水库流域氮、磷湿沉降对水库水体营养的贡献率,本研究对2014 2015年的汤浦水库流域4个采样点的雨水及3条溪流进行样品收集,测定其中磷和不同形态氮的质量浓度,分析汤浦水库流域大气湿沉降中氮、磷营养盐的分布特征,并估算氮、磷营养盐湿沉降对汤浦水库入库负荷的贡献率.结果表明:湿沉降中总氮(TN)平均浓度为1.02±0.58 mg/L,氨氮、硝态氮和有机氮浓度占TN浓度的比例分别为60.65%、34.07%和5.28%;总磷(TP)平均浓度为0.033±0.028 mg/L.4个采样点湿沉降中氮、磷浓度均表现为冬春季(少雨季)高、夏秋季(多雨季)低.空间上,王化点位的各形态氮和总磷浓度显著高于其他3个采样点.TN和TP年均湿沉降通量约为18.15和0.62 kg/(hm~2·a),年均沉降总量为834.94和28.39 t;库区TN和TP水面湿沉降量为24.14和0.82 t,直接贡献率占河流输入的1.77%和3.07%.湿沉降来源的氮、磷营养盐随河流输入的间接贡献率为8.3%和4.6%.综上所述,氮、磷湿沉降是水库外源营养的重要输入部分,深入掌握其时空分布特征及入库贡献率是进一步加强流域管理和减轻水库外源营养输入的重要前提.     

基于Fabry-Perot的中高层大气风速反演数据处理研究

中高层大气风速反演需要精确的确定法布里-帕罗干涉仪(Fabry-Perot Interferometer,FPI)干涉条纹的圆心和半径.本文针对FPI非闭合式干涉环条纹,提出了新的条纹圆心和半径确定方法:首先对所得到的条纹强度分布进行噪声去除预处理:包括均值滤波和自适应滤波;然后初步确定圆心,以该圆心为中心作n条射线得到n条干涉环剖线,利用高斯函数拟合得到干涉环峰值位置,再利用所得峰值位置进行圆拟合得到新的圆心和半径;最后以新的圆心为初始圆心重复上述计算过程直到圆心坐标收敛.利用上述方法对FPI仿真数据进行处理,并用于中高层大气风速反演,得到风速值为96.9537 m/s(对应实际风速值约100 m/s)和7.528.2 m/s (对应实际风速值约10 m/s),将其与理论实际值进行比较,得到反演绝对误差分别为-2.977 m/s和-2.465 m/s,相对误差分别为-2.98%和-24.67%,表明上述方法满足中高层大气风速(一般为每秒几十米到几百米)的反演精度要求,初步论证了圆心和半径确定方法的可行性.     

Analytical and semi-analytical solutions of horizontal well capture times under no-flow and constant-head boundaries

The closed-form analytical solutions and semi-analytical solutions of capture times to horizontal wells are derived for different recovery scenarios. The capture time is the time a fluid particle takes to flow to the well. The first scenario is recovery from a confined aquifer in which the influence of regional groundwater flow upon the capture time is included. The second scenario is recovery from underneath a water reservoir in which the top boundary of the aquifer is constant-head. The third scenario is recovery from a low-permeability layer bounded above and below by much higher permeability media. Closed-form solutions are provided for the cases with: (1) a center or a bottom well for the first scenario; (2) a bottom well for the second scenario; and (3) a center well for the third scenario. Semi-analytical solutions are provided for general well locations for those scenarios. Solutions for both isotropic and anisotropic media are studied. These solutions can be used as quick references to calculate the capture times, and as benchmarks to validate numerical solutions. The limitations of the analytical solutions are analyzed. Our results show that the top and bottom no-flow boundaries of an aquifer constrain the vertical flow, but enhance the horizontal flow, resulting in elongated iso-capture time curves. When constant-head boundaries are presented, water can infiltrate vertically across those boundaries to replenish the aquifers, resulting in less elongated iso-capture time curves.     

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.     

Stable isotopes of atmospheric water vapour and precipitation in the northeast Qinghai‐Tibetan Plateau

Stable water isotopes (δ¹⁸O and δ²H) are an important source signature for understanding the hydrological cycle and altered climate regimes. However, the mechanisms underlying atmospheric water vapour isotopes in the northeast Qinghai‐Tibetan Plateau of central Asia remain poorly understood. This study initially investigated water vapour isotopic composition and its controls during the premonsoon and monsoon seasons. Isotopic compositions of water vapour and precipitation exhibited high variability across seasons, with the most negative average δ¹⁸O values of precipitation and the most positive δ¹⁸O values of water vapour found during the premonsoon periods. Temperature effect was significant during the premonsoon period but not the monsoon period. Both a higher slope and intercept of the local meteoric water line were found during the monsoon period as compared with in the premonsoon period, suggesting that raindrops have been experienced a greater kinetic fractionation process such as reevaporation below the cloud during the premonsoon periods. The δ²H and δ¹⁸O signatures in atmospheric water vapour tended to be depleted with the occurrence of precipitation events especially during the monsoon period and probably as a result of rainout processes. The monthly average contribution of evaporation from the lake to local precipitation was 35.2%. High d‐excess values of water vapour were influenced by the high proportion of local moisture mixing, as indicated by the gradually increasing relative humidity along westerly and Asian monsoon trajectories. The daily observation (observed ε) showed deviations from the equilibrium fractionation factors (calculated ε), implying that raindrops experienced substantial evaporative enrichment during their descent. The average fraction of raindrops reevaporation was estimated to be 16.4± 12.9%. These findings provide useful insights for understanding the interaction between water vapour and precipitation, moisture sources, and help in reconstructing the paleoclimate in the alpine regions.     

Global aridification in the second half of the 20th century and its relationship to large-scale climate background

The variation in surface wetness index (SWI), which was derived from global gridded monthly precipi- tation and monthly mean surface air temperature datasets of Climatic Research Unit (CRU), from 1951― 2002 over global land was analyzed in this paper. The characteristics of the SWI variation in global continents, such as North America, South America, Eurasia, Africa, and Australia, were compared. In addition, the correlation between the SWI variation of each continent (or across the globe) and the large-scale background closely related to SST variations, which affects climate change, was analyzed. The results indicate that the SWI variation shows distinct regional characteristics in the second half of the 20th century under global warming. A drying trend in the last 52 years occurred in Africa, Eurasia, Australia and South America, most obviously in Africa and Eurasia. North America shows a wetting trend after 1976. A 30-year period of dry-wet oscillation is found in South America and Australia; the latest is in a drying period in two regions. The results also revealed that global warming has changed the dry-wet pattern of the global land. South America and Australia have a drying trend despite in- creases in precipitation. This indicates that increases in surface air temperature cannot be ignored in aridification studies. Global dry-wet variation is closely related to large-scale SST variations: the drying trend in Africa and Eurasia and the wetting trend in North America are correlated with Pacific Decadal Oscillation (PDO); the interdecadal oscillation of SWI in South America and Australia is consistent with the interdecadal variation in Southern Oscillation Index (SOI).     

Time–space fractional governing equations of one‐dimensional unsteady open channel flow process: Numerical solution and exploration

Although fractional integration and differentiation have found many applications in various fields of science, such as physics, finance, bioengineering, continuum mechanics, and hydrology, their engineering applications, especially in the field of fluid flow processes, are rather limited. In this study, a finite difference numerical approach is proposed to solve the time–space fractional governing equations of 1‐dimensional unsteady/non‐uniform open channel flow process. By numerical simulations, results of the proposed fractional governing equations of the open channel flow process were compared with those of the standard Saint‐Venant equations. Numerical simulations showed that flow discharge and water depth can exhibit heavier tails in downstream locations as space and time fractional derivative powers decrease from 1. The fractional governing equations under consideration are generalizations of the well‐known Saint‐Venant equations, which are written in the integer differentiation framework. The new governing equations in the fractional‐order differentiation framework have the capability of modelling nonlocal flow processes both in time and in space by taking the global correlations into consideration. Furthermore, the generalized flow process may possibly shed light on understanding the theory of the anomalous transport processes and observed heavy‐tailed distributions of particle displacements in transport processes.     

Temporal and spacial analysis of regional composite nodal plane solutions for small earthquakes

A method is proposed in this paper for the analysis of temporal and spatial characteristics of composite nodal plane solutions for small earthquakes. With this method, the interested region is devided into small areas according to the geological features of the region. As an example, 107 composite nodal plane solutions are calculated for the adjoining region of Shaxi, Hebei and Neimenggu. The temporal and spatial characteristics of the variations of the solution parameters before and after the great Tangshan main earthquake in 1976 have been analysed and some interesting results are obtained. The Chinese version of this paper appeared in the Chinese edition ofActa Seismlogica Sinica,13, 9–20, 1991.