On the sensitivity of the results of least-squares adjustments concerning the stochastic model

A proper perturbation theory of a mathematical model and the quantities derived by means of least-squares adjustments is indispensable if the results have to be interpreted in a wider context. The sensitivity of some characteristic results of least-squares adjustments such as the estimated values of the parameters and their variance–covariance matrix due to imminent uncertainties of the stochastic model is discussed in detail. Linearizations are used with rigorous error measures and interval mathematics. Numerical examples conclude the investigations. Received: 27 December 1997 / Accepted: 19 April 1999     

海洋温带气旋爆发性发展数值试验

利用 Ｐ Ｓ Ｕ／ Ｎ Ｃ Ａ Ｒ Ｍ Ｍ ４ 对５ 个西北太平洋温带气旋的爆发性发展进行了一系列数值模拟和敏感性试验,并对重要的物理过程进行了分析和诊断。采用相同物理过程及边界条件的控制试验成功地模拟出了主要的爆发性气旋加深率,为海洋爆发性气旋的业务数值预报提供了可能。敏感性试验获得了湿物理过程、能量频散、 Ｓ Ｓ Ｔ 和海面能通量、日本岛地形及初、边值条件等影响气旋加深率的定量认识,分析表明水的微物理过程,特别是网格尺度的水汽凝结、未饱和层的云滴和雨滴蒸发,是气旋爆发性发展中最重要的物理过程;在高空 ２００～３００ｈ Ｐａ 层的云滴蒸发效应可能是形成相应层气旋中心非绝热冷却峰值的主要原因;由内在热力动力学过程所决定的潜热释放比对流参数化任意规定的加热分布更接近实际并能产生更好的模拟结果;没有能量频散效应时可减小模拟加深的 ３０％ ;海面能通量在初始时刻比在爆发性发展时更重要,不计初始时海面能通量将影响模拟加深约 ２５％ ,而不计爆发性发展时的海面能通量,这种影响不及前者的一半;爆发性发展时的海面能通量呈不均匀分布并能诱导反锋面热力环流在局部抑制气旋的加深;大气模式对海气边界层能通量交换的变化和海洋增暖产生了显著的热力学响     

Global sensitivity analysis for a numerical model of radionuclide migration from the RRC “Kurchatov Institute” radwaste disposal site

Today, in different countries, there exist sites with contaminated groundwater formed as a result of inappropriate handling or disposal of hazardous materials or wastes. Numerical modeling of such sites is an important tool for a correct prediction of contamination plume spreading and an assessment of environmental risks associated with the site. Many uncertainties are associated with a part of the parameters and the initial conditions of such environmental numerical models. Statistical techniques are useful to deal with these uncertainties. This paper describes the methods of uncertainty propagation and global sensitivity analysis that are applied to a numerical model of radionuclide migration in a sandy aquifer in the area of the RRC “Kurchatov Institute” radwaste disposal site in Moscow, Russia. We consider 20 uncertain input parameters of the model and 20 output variables (contaminant concentration in the observation wells predicted by the model for the end of 2010). Monte Carlo simulations allow calculating uncertainty in the output values and analyzing the linearity and the monotony of the relations between input and output variables. For the non monotonic relations, sensitivity analyses are classically done with the Sobol sensitivity indices. The originality of this study is the use of modern surrogate models (called response surfaces), the boosting regression trees, constructed for each output variable, to calculate the Sobol indices by the Monte Carlo method. It is thus shown that the most influential parameters of the model are distribution coefficients and infiltration rate in the zone of strong pipe leaks on the site. Improvement of these parameters would considerably reduce the model prediction uncertainty.     

套后介质声学性质对套管中三种模式波影响的对比分析

由于套管的厚度小于目前声波测井仪器工作频率下的波长,声波仪器工作时可在套管中激发Lamb波或SH模式波.目前评价水泥胶结质量的声波测井仪器主要是利用套管中的对称Lamb波(拉伸波,S0模式)或反对称Lamb波(泄漏弯曲波,A0模式)的相对幅度或衰减评价套管与水泥之间的胶结程度.Lamb波可看作是纵波和横波在套管边界的耦合形成的,在套管中还存在另一种非耦合的SH横波,偏振方向与套管轴向平行沿着周向传播.本文基于定向声源辐射技术,实现了对称Lamb波、反对称Lamb波的分波模拟技术,数值研究了套管后耦合不同声阻抗介质时,对称Lamb波、反对称Lamb波以及SH横波的测井响应,通过频散衰减曲线以及模式波的波形响应幅度的直观显示表明,由于套管中的SH波仅向固体水泥中辐射剪切波,这一传播特征与套管中的Lamb波相比可以极大提高套管-水泥界面胶结状况的测量灵敏度.Lamb波的固有缺陷是套管与两侧介质的较大声阻抗反差使得在井中测量套管后面水泥界面的灵敏度受到相当大的限制.     

高灵敏度感应式磁传感器测试研究

本文着重对研制的感应式磁传感器的本底噪声和灵敏度特性进行测试研究,在平行噪声测试方法（NPI）基础上设计了针对本研究的磁传感器噪声测试方法,测试结果表明：MC-30的噪声水平1 Hz时为0.3 pT/√Hz,10 Hz时为0.03 pT/√Hz,100 Hz时为10 fT/√Hz,1 kHz时为3 fT/√Hz,灵敏度为215 mV/nT;MC-50的噪声水平0.01 Hz时为10 pT/√Hz,1 Hz时为0.05 pT/√Hz,10 Hz时为10 fT/√Hz,100 Hz时为0.5 fT/√Hz,灵敏度为1359 mV/nT.除此之外,通过野外试验对比及工程应用验证了MC-30和MC-50具备良好的测量精度及野外工作性能,能够满足实际电磁勘探任务的需要.     

Use of steady-state concentration measurements in geostatistical inversion

In geostatistical inverse modeling, hydrogeological parameters, such as hydraulic conductivity, are estimated as spatial fields. Upon discretization this results in several thousand (log-)hydraulic conductivity values to be estimated. Common inversion schemes rely on gradient-based parameter estimation methods which require the sensitivity of all measurements with respect to all parameters. Point-like measurements of steady-state concentration in aquifers are generally not well suited for gradient-based methods, because typical plumes exhibit only a very narrow fringe at which the concentration decreases from a maximal value to zero. Only here the sensitivity of concentration with respect to hydraulic conductivity significantly differs from zero. Thus, if point-like measurements of steady-state concentration do not lie in this narrow fringe, their sensitivity with respect to hydraulic conductivity is zero. Observations of concentrations averaged over a larger control volume, by contrast, show a more regular sensitivity pattern. We thus suggest artificially increasing the sampling volume of steady-state concentration measurements for the evaluation of sensitivities in early stages of an iterative parameter estimation scheme. We present criteria for the extent of artificially increasing the sampling volume and for decreasing it when the simulation results converge to the measurements. By this procedure, we achieve high stability in geostatistical inversion of steady-state concentration measurements. The uncertainty of the estimated parameter fields is evaluated by generating conditional realizations.     

Identifying the effects of parameter uncertainty on the reliability of riverbank stability modelling

Bank retreat is a key process in fluvial dynamics affecting a wide range of physical, ecological and socioeconomic issues in the fluvial environment. To predict the undesirable effects of bank retreat and to inform effective measures to prevent it, a wide range of bank stability models have been presented in the literature. These models typically express bank stability by defining a factor of safety as the ratio of driving and resisting forces acting on the incipient failure block. These forces are affected by a range of controlling factors that include such aspects as the bank profile (bank height and angle), the geotechnical properties of the bank materials, as well as the hydrological status of the riverbanks. In this paper we evaluate the extent to which uncertainties in the parameterization of these controlling factors feed through to influence the reliability of the resulting bank stability estimate. This is achieved by employing a simple model of riverbank stability with respect to planar failure (which is the most common type of bank stability model) in a series of sensitivity tests and Monte Carlo analyses to identify, for each model parameter, the range of values that induce significant changes in the simulated factor of safety. These identified parameter value ranges are compared to empirically derived parameter uncertainties to determine whether they are likely to confound the reliability of the resulting bank stability calculations. Our results show that parameter uncertainties are typically high enough that the likelihood of generating unreliable predictions is typically very high (>  80% for predictions requiring a precision of < ± 15%). Because parameter uncertainties are derived primarily from the natural variability of the parameters, rather than measurement errors, much more careful attention should be paid to field sampling strategies, such that the parameter uncertainties and consequent prediction unreliabilities can be quantified more robustly.     

基于网格数据的贵州土壤侵蚀敏感性评价及其空间分异

在通用土壤侵蚀方程的基础上,建立了土壤侵蚀敏感性评价指标体系,利用GIS方法对影响土壤侵蚀敏感性的单因子进行评价,并将各因子进行网格化,运用网格数据的空间叠加分析方法对贵州省土壤侵蚀敏感性进行综合评价。在此基础上探讨了贵州省土壤侵蚀敏感性空间分异规律。通过与已有的土壤侵蚀现状图比较,发现土壤侵蚀高敏感区与水土流失严重区并不吻合,并进一步指出,脆弱的喀斯特环境是产生严重水土流失和导致石漠化的地质基础,强烈的人类活动是加速这一过程的主要驱动力量。      

S/P模式计算的冷却塔烟气抬升高度敏感性试验

德国VDI3784的S/P模式为三维流体动力学积分模式,其方程主要描述了无穷小体积元素的质量、动量、静态污染物质量浓度及能量的守恒。利用德国模式进行了冷却塔烟气排放不同参数、不同大气条件下烟气抬升高度的敏感性试验。结果表明：在影响烟气抬升高度的3个气象要素（风速,气温和湿度）中,风速和气温的变化对结果影响较大,而湿度影响较小。在D类稳定度,当环境风速从0.1 m/s增加到15.0 m/s时,抬升高度将从711.7 m变为38.5 m。随着环境温度的升高,抬升高度明显单调变小;当稳定度为A类,环境温度从10℃升到40℃时,烟气抬升最大高度从688.9 m降低到45.1 m,降低了14倍多。而环境湿度的变化,对抬升高度的影响不是很明显。对于E和F类,当环境湿度从20 %增加到70 %,最大抬升高度分别从115.3 m和84.6m降到112.9 m和81.7m,分别降低了3.43 %和2.08 %。在影响烟气抬升高度的其他3个因素（凉水塔直径,烟气出口速度和混合气体温度）中,混合气体温度的变化对结果影响较大,而凉水塔直径和烟气出口速度的影响较小。在各类稳定度条件下,当出口温度从20 ℃变到90 ℃时,烟气抬升高度增加1.2-13.3倍;在各类稳定度条件下,当凉水塔直径从30 m变到90 m,烟气抬升高度仅增加0.63-1.40倍;在各类稳定度条件下,当出口速度从2.5 m/s变到8 m/s,烟气抬升高度增加0.24-0.74倍。