Rainfall network design using kriging and entropy

The spatial distribution of rainfall is related to meteorological and topographical factors. An understanding of the weather and topography is required to select the locations of the rain gauge stations in the catchment to obtain the optimum information. In theory, a well‐designed rainfall network can accurately represent and provide the needed information of rainfall in the catchment. However, the available rainfall data are rarely adequate in the mountainous area of Taiwan. In order to provide enough rainfall data to assure the success of water projects, the rainfall network based on the existing rain gauge stations has to be redesigned. A method composed of kriging and entropy that can determine the optimum number and spatial distribution of rain gauge stations in catchments is proposed. Kriging as an interpolator, which performs linear averaging to reconstruct the rainfall over the catchment on the basis of the observed rainfall, is used to compute the spatial variations of rainfall. Thus, the rainfall data at the locations of the candidate rain gauge stations can be reconstructed. The information entropy reveals the rainfall information of the each rain gauge station in the catchment. By calculating the joint entropy and the transmitted information, the candidate rain gauge stations are prioritized. In addition, the saturation of rainfall information can be used to add or remove the rain gauge stations. Thus, the optimum spatial distribution and the minimum number of rain gauge stations in the network can be determined. The catchment of the Shimen Reservoir in Taiwan is used to illustrate the method. The result shows that only seven rain gauge stations are needed to provide the necessary information. Copyright © 2007 John Wiley & Sons, Ltd.     

Dam overtopping risk assessment considering inspection program

Safety inspection of large dams in Taiwan is conducted every 5 years. The practice does not take into consideration uncertainty of dam conditions. The goal of this study is to determine the optimal dam inspection interval under the consideration of overtopping risk incorporating uncertainty gate availability. In earlier studies, assessment of overtopping risk only considered the uncertainties in reservoir properties and natural randomness of hydrologic events without giving much thought to the availability of spillway gates. As a result, the overtopping risk could be underestimated. In this study, an innovative concept is proposed to evaluate dam overtopping by taking into account spillway gate availability. The framework consists of three parts: (1) evaluation of conditional overtopping risk for different numbers of malfunctioning spillway gates; (2) evaluation of spillway gate availability; and (3) dam inspection scheduling. Furthermore, considerations are given to overtopping risk, inspection cost, and dam break cost for determining the optimal inspection schedule. The methodology is applied to the Shihmen Reservoir in Taiwan and to evaluate its time-dependent overtopping risk. Results show that overtopping risk considering the availability of the spillway gates is higher than the one without considering the availability of the spillway gates.     

Analysis of tracer tomography using temporal moments of tracer breakthrough curves

Hydraulic/partitioning tracer tomography (HPTT) was recently developed by Yeh and Zhu [Yeh T-CJ, Zhu J. Hydraulic/partitioning tracer tomography for characterization of dense nonaqueous phase liquid source zones, Water Resour Res 2007;43:W06435. doi:10.1029/2006WR004877.] for estimating spatial distribution of dense nonaqueous phase liquids (DNAPLs) in the subsurface. Since discrete tracer concentration data are directly utilized for the estimation of DNAPLs, this approach solves the hyperbolic convection–dispersion equation. Solution to the convection–dispersion equation however demands fine temporal and spatial discretization, resulting in high computational cost for an HPTT analysis. In this work, we use temporal moments of tracer breakthrough curves instead of discrete concentration data to estimate DNAPL distribution. This approach solves time independent partial differential equations of the temporal moments, and therefore avoids solving the convection–dispersion equation using a time marching scheme, resulting in a dramatic reduction of computational cost. To reduce numerical oscillations associated with convection dominated transport problems such as in inter-well tracer tests, the approach uses a finite element solver adopting the streamline upwind Petrov–Galerkin method to calculate moments and sensitivities. We test the temporal moment approach through numerical simulations. Comparing the computational costs between utilizing moments and discrete concentrations, we find that temporal moments significantly reduce the computation time. We also find that tracer moment data collected through a tomographic survey alone are able to yield reasonable estimates of hydraulic conductivity, as indicated by a correlation of 0.588 between estimated and true hydraulic conductivity fields in the synthetic case study.     

Stochastic analysis of bounded unsaturated flow in heterogeneous aquifers: Spectral/perturbation approach

This paper describes a stochastic analysis of steady state flow in a bounded, partially saturated heterogeneous porous medium subject to distributed infiltration. The presence of boundary conditions leads to non-uniformity in the mean unsaturated flow, which in turn causes non-stationarity in the statistics of velocity fields. Motivated by this, our aim is to investigate the impact of boundary conditions on the behavior of field-scale unsaturated flow. Within the framework of spectral theory based on Fourier–Stieltjes representations for the perturbed quantities, the general expressions for the pressure head variance, variance of log unsaturated hydraulic conductivity and variance of the specific discharge are presented in the wave number domain. Closed-form expressions are developed for the simplified case of statistical isotropy of the log hydraulic conductivity field with a constant soil pore-size distribution parameter. These expressions allow us to investigate the impact of the boundary conditions, namely the vertical infiltration from the soil surface and a prescribed pressure head at a certain depth below the soil surface. It is found that the boundary conditions are critical in predicting uncertainty in bounded unsaturated flow. Our analytical expression for the pressure head variance in a one-dimensional, heterogeneous flow domain, developed using a nonstationary spectral representation approach [Li S-G, McLaughlin D. A nonstationary spectral method for solving stochastic groundwater problems: unconditional analysis. Water Resour Res 1991;27(7):1589–605; Li S-G, McLaughlin D. Using the nonstationary spectral method to analyze flow through heterogeneous trending media. Water Resour Res 1995; 31(3):541–51], is precisely equivalent to the published result of Lu et al. [Lu Z, Zhang D. Analytical solutions to steady state unsaturated flow in layered, randomly heterogeneous soils via Kirchhoff transformation. Adv Water Resour 2004;27:775–84].     

一个与铬铁矿富集有关的巨型实验

现在岩石学、矿床学的实验一般用样品是几十毫克、甚至十几毫克,其目的是要精确化。但是许多事实说明,这种精密的实验工作并不能完全解决矿床的成因。要解决矿床成因的问题,至少必须回答下面三个问题:(1)有用金属矿物是在什么条件下形成的;(2)有用金属矿物是如何富集为矿石的;(3)矿石如何具有一定的量,并达到经济上可开采的要求。实验岩石学和实验矿床学的资料一般只说明了第一个问题。     

沉积矿床成矿时代的地史意义

地质工作者研究矿床的意义,不仅在于认识矿床的形成与组成,不仅在于说明矿床的存在状况,还在于深入矿床的本质,指出找矿预测的途径;结合生产斗争实践,为社会主义革命和社会主义建设服务。     

滇西南澜沧群多硅白云母的多型和化学成分特征及其意义

从理论、实验及实际观察的结果都表明,随着压力的增加白云母中绿鳞石的含量显著地增加,可以认为在多期变质作用过程中,尤其是在变质压力不同的多期变质作用下,形成的多硅白云母,其化学成分就会打上不同的烙印。７７个多硅白云母化学成分的统计结果表明,澜沧群低级变质岩中的多硅白云母有两种成因。在Ｎａ－Ｍｇ相关图上,反映了高压和中压变质特征,高压变质的多硅白云母约占７０％。这与用多硅白云母ｂ０值鉴别的高压和中压变质是相吻合的。多硅白云母的多型为３Ｔ和２Ｍ１型,以２Ｍ１型为主     

钙钛矿型结构亚硝酸盐和氰化物的分子体积

绝大部分的亚硝酸盐和氰化物属于钙钛矿型结构,但有部分化合物为“反”钙钛矿型结构,充填空洞A位的阳离子的拓扑体积为0。阴离子团NO2-和CN-的拓扑体积都近乎常数,分别为41.73Å3和40.03Å3,标准方差σn-1=1.516和σn-1=1.25。由此,进一步证明了原来的一套离子拓扑体积数值的普适性。“反”钙钛矿型结构中A位阳离子的平均半径rA>1.00Å时,三价阳离子会产生扩容效应,其扩容系数大约是其本身拓扑体积的2倍;正钙钛矿型结构中,当A位是由半径较大的Cs+充填时,Cs+也会产生扩容效应,其扩容系数约为24Å3。氰化物中结晶水分子的拓扑体积近乎常数,为24Å3或0。     

Hydromagnetic buoyancy force in the solar atmosphere

An extraneous magnetized body, either a flux tube or a plasmoid, immersed in the solar atmosphere is subjected to a hydromagnetic buoyancy force. It results from the peripheral inhomogeneity of ambient hydromagnetic pressure, which is caused or enhanced by the presence of the extraneous body. This extra-caused force acts at various mass elements of the immersed body through its distribution as a nearly uniform force density, just like the gravitational force. Since hydromagnetic buoyancy force comprises hydrostatic buoyancy force, hydrodynamic lift force, and magnetostatic diamagnetic force, this constitutes a magnetohydrodynamic generalization of Archimedes' principle which deals with hydrostatic buoyancy force.In the solar atmosphere hydromagnetic buoyancy force has an obliquely upward direction, with a component in the direction opposite to the downward gravity. It provides an upward force to counterbalance or even to exceed the downward gravitational force. Such an upward force is the dynamic cause for the stationary equilibrium of quiescent prominences and outward motion of coronal transients.