An approximate Riemann solver for sensitivity equations with discontinuous solutions

The sensitivity of a model output (called a variable) to a parameter can be defined as the partial derivative of the variable with respect to the parameter. When the governing equations are not differentiable with respect to this parameter, problems arise in the numerical solution of the sensitivity equations, such as locally infinite values or instability. An approximate Riemann solver is thus proposed for direct sensitivity calculation for hyperbolic systems of conservation laws in the presence of discontinuous solutions. The proposed approach uses an extra source term in the form of a Dirac function to restore sensitivity balance across the shocks. It is valid for systems such as the Euler equations for gas dynamics or the shallow water equations for free surface flow. The method is first detailed and its application to the shallow water equations is proposed, with some test cases such as dike- or dam-break problems with or without source terms. An application to a two-dimensional flow problem illustrates the superiority of direct sensitivity calculation over the classical empirical approach.     

时间域航空电磁2.5维非线性共轭梯度反演

对于时间域航空电磁法二维和三维反演来说,最大的困难在于有效的算法和大的计算量需求.本文利用非线性共轭梯度法实现了时间域航空电磁法2.5维反演方法,着重解决了迭代反演过程中灵敏度矩阵计算、最佳迭代步长计算、初始模型选取等问题.在正演计算中,我们采用有限元法求解拉式傅氏域中的电磁场偏微分方程,再通过逆拉氏和逆傅氏变换高精度数值算法得到时间域电磁响应.在灵敏度矩阵计算中,采用了基于拉式傅氏双变换的伴随方程法,时间消耗只需计算两次正演,从而节约了大量计算时间.对于最佳步长计算,二次插值向后追踪法能够保证反演迭代的稳定性.设计两个理论模型,检验反演算法的有效性,并讨论了选择不同初始模型对反演结果的影响.模型算例表明:非线性共轭梯度方法应用于时间域航空电磁2.5维反演中稳定可靠,反演结果能够有效地反映地下真实电性结构.当选择的初始模型电阻率值与真实背景电阻率值接近时,能得到较好的反演结果,当初始模型电阻率远大于或远小于真实背景电阻率值时反演效果就会变差.     

基于Born敏感核函数的速度、密度双参数全波形反演

速度、密度之间的相互耦合使得密度在多参数全波形反演中较难获得.本文将截断高斯-牛顿法用于声介质速度、密度双参数全波形反演,通过考虑近似Hessian矩阵中反映速度、密度相互作用的非主对角块元素,有效解决了多参数全波形反演中速度、密度之间的耦合问题,在不采用反演策略的情况下,仍能够获得精度较高的速度、密度反演结果.常规的截断牛顿类全波形反演通常利用一阶伴随状态法求取目标函数对模型参数的梯度,利用二阶伴随状态法或有限差分法求解Hessian-向量乘,在每一步内循环迭代过程中需要额外求解两次正演问题,计算量较大.本文基于Born近似,将梯度计算中的核函数-向量乘表示为具有明确物理意义的向量-标量乘的累加运算,同时将Hessian-向量乘转化为两次核函数-向量乘,无需额外求解正演问题,有效降低了计算量.数值实验证明了本文提出的方法的有效性.     

VTI介质多参数联合走时层析成像方法

本文基于球谐展开群速度表达式计算走时关于各向异性参数的Fréchet核函数,利用共轭梯度法对两种参数化方法进行了VTI介质中多参数联合反演方法研究.经过理论分析和数值试验发现,与经典的Thomsen参数化方法相比,垂直慢度、水平慢度与动校正慢度的参数化方式更有利于VTI介质多参数联合走时层析反演.为了克服走时对ε参数的不敏感性,我们采用了两步法进行双参数反演,理论模型试验反演得到了与垂直速度精度相当的ε参数.可以将两步法扩展到三步法以同时反演各向异性介质中的三个参数,数值试验展示了该策略的应用潜力.     

Comprehensive three dimensional finite element analysis,parametric study and sensitivity analysis on the seismic performance of soil–micropile-superstructure interaction

A comprehensive dynamic three dimensional finite element model, which includes the effect of lots of important parameters on the micropiles seismic performance, has been presented. The validation of the built model has been carried out using remodeling a single degree of freedom shaking table test done by Mc Manus at the University of Canterbury. The gained results proved the accuracy of the constructed model. Then, using the parametric analysis, effects of all the earthquake characteristics, soil properties, superstructure and micropiles' cap and micropiles structure on the seismic performance of micropiles have been investigated by means of presenting internal forces and displacements which occurred as the main result of earthquake. Furthermore, using the data analysis, the most and the least influential parameters on internal forces are obtained based on the Cosine Amplitude Method (CAM).     

阿勒泰山脉对新疆北部地区强暴雪过程影响的数值模拟研究

本文利用中尺度数值模式WRFV3.1对2010年1月6-8日新疆阿勒泰地区的强暴雪过程进行了敏感性数值模拟实验,来研究阿勒泰山脉地形对此次暴雪的影响。结果表明,阿勒泰地形对此次暴雪过程的形成和发展有明显的作用：（1）削减阿勒泰地区地形20%后,在阿勒泰山脉以西会导致降水减少,而在其以东则会导致降水增加;（2）对流层低层垂直速度的分布显示,在此次暴雪过程中,阿勒泰地区存在由于山脉地形引起的地形波,削减地形后会导致山脉地形波的强度减弱;（3）削减阿勒泰地区的地形后,在对流层低层700hPa,会出现气旋式环流增强的特征,而涡度场的表现则比较凌乱,同时也会对水汽场及云微物理量场产生影响。     

Sensitivity Evaluation of Snow Simulation to Multi-parameterization Schemes in the Noah-MP Model

On account of the latest community Noah land surface model with multi-parameterization (Noah-MP) schemes and its uncertainty breadth in simulation results being difficult to be determined, this study assessed the sensitivity of snow to physics options using meteorological data from the Altay Station in northern Xinjiang. The Noah-MP physics ensemble simulation with the total number of 13 824 was designed without the consideration of the uncertainties of forcing data and parameters. The natural selection approach was used to analyze the sensitivity of physical processes. Based on the results of sensitivity analysis, the uncertainty of ensemble simulation results was further discussed. The results showed that snow was sensitive to the physical processes of surface-layer exchange coefficient, partitioning precipitation into rainfall and snowfall, lower boundary condition of soil temperature, and first-layer snow or soil temperature time scheme; Uncertainties in multi-parameterization ensemble simulation experiments were mainly from sensitive physical processes under the condition of disregarding uncertainties of forcing data and parameters. After removing the parameterization schemes that notably reduced simulation performance in sensitive physical processes, the uncertainty breadth in ensemble simulations decreased significantly. Finally, an optimal combination group of parameterization schemes for this station was configured.     

Biological reduction of chlorinated solvents: Batch-scale geochemical modeling

Simulation of biodegradation of chlorinated solvents in dense non-aqueous phase liquid (DNAPL) source zones requires a model that accounts for the complexity of processes involved and that is consistent with available laboratory studies. This paper describes such a comprehensive modeling framework that includes microbially mediated degradation processes, microbial population growth and decay, geochemical reactions, as well as interphase mass transfer processes such as DNAPL dissolution, gas formation and mineral precipitation/dissolution. All these processes can be in equilibrium or kinetically controlled. A batch modeling example was presented where the degradation of trichloroethene (TCE) and its byproducts and concomitant reactions (e.g., electron donor fermentation, sulfate reduction, pH buffering by calcite dissolution) were simulated. Local and global sensitivity analysis techniques were applied to delineate the dominant model parameters and processes. Sensitivity analysis indicated that accurate values for parameters related to dichloroethene (DCE) and vinyl chloride (VC) degradation (i.e., DCE and VC maximum utilization rates, yield due to DCE utilization, decay rate for DCE/VC dechlorinators) are important for prediction of the overall dechlorination time. These parameters influence the maximum growth rate of the DCE and VC dechlorinating microorganisms and, thus, the time required for a small initial population to reach a sufficient concentration to significantly affect the overall rate of dechlorination. Self-inhibition of chlorinated ethenes at high concentrations and natural buffering provided by the sediment were also shown to significantly influence the dechlorination time. Furthermore, the analysis indicated that the rates of the competing, nonchlorinated electron-accepting processes relative to the dechlorination kinetics also affect the overall dechlorination time. Results demonstrated that the model developed is a flexible research tool that is able to provide valuable insight into the fundamental processes and their complex interactions during bioremediation of chlorinated ethenes in DNAPL source zones.     

Establishing a monitoring network for an impoundment-induced landslide in Three Gorges Reservoir Area, China

A methodology for monitoring system of an impoundment-induced landslide in Three Gorges Reservoir Area, China is introduced. Currently, based on landslide geological classification, the monitoring regions and methods which include types of monitoring instruments, placement and calibration precision of instruments, and appropriate periods for instrumental placement is confirmed. To optimize the monitoring system, sensitivity analysis of displacements and the water table in landslides affected by reservoir surface fluctuation is completed to determine the layout of the monitoring cross sections and the monitoring points. As a case study, the behavior of displacements and the potential fluctuation of the water table in the Shiliushubao landslide, produced by the gradual water impoundment at Three Gorges Reservoir, has been simulated using 3D finite element method analysis. The sensitivity analysis of Shiliushubao landslide is investigated by the fuzzy set evaluation method. As a result, the monitoring network of Shiliushubao landslide is established.     

大尺度辐射度模型敏感性分析及在祁连山林区的应用

辐射度模型(RGM)用于计算植被二向性反射(BRDF)。但是目前基于辐射度方法的计算机模拟模型的应用被局限在较小的、比较单一的场景范围之内。把RGM模型扩展为大场景辐射度模型(LRGM),关键在于如何把大场景分为子场景,既保证模拟精度,又可以显著缩短计算时间。通过不同地形条件下模拟结果的对比,分析讨论了子场景划分方法的敏感性,分析表明:①地形对BRDF是有影响的,主要表现在后向观测方向的增强作用和前向观测方向的减弱作用;②子场景个数对模拟结果影响不大,最大偏差不超过0.007。然后,选取黑河流域大野口山区水源涵养林带为观测试验区,利用大场景辐射度模型进行真实结构模拟,将模拟结果与ASTER数据进行对比,结果表明,二者最大绝对误差不超过0.0382,证明LRGM模型模拟遥感像元尺度的BRDF是可行的。