A study on terrain-induced tropical cyclone looping in East Taiwan: case study of Typhoon Haitang in 2005

A mesoscale mountain such as the Central Mountain Range (CMR) of Taiwan can considerably affect the motion and the structure of an approaching tropical cyclone in very complicated ways. Many studies have presented and explained the mechanism for the change of moving speed, track deflection, or track discontinuity. In the past, the tracks of Typhoon Mary (1965), Tropical Cyclone Polly (1993), and Typhoon Haitang (2005) have a looping motion prior to making landfall on Taiwan. When the looping occurs, the timing and the intensity of the typhoon to affect Taiwan can be very different from the one moving with smooth track. It is very important to have a correct forecast for disaster mitigation operations. However, the mechanism causing such looping has not been fully understood. In this study, the case of Typhoon Haitang is examined. The radar reflectivity diagrams are used to illustrate looping in its track. By applying piecewise potential vorticity inversion analysis and numerical model simulations, it is shown that the looping motion of Typhoon Haitang near Taiwan resulted from the CMR terrain effect. When Typhoon Haitang approaches Taiwan and its circulation encounters the CMR, the terrain induces a cyclonic vortex in the lee side of the mountain over southeast of Taiwan. This terrain-induced vortex interacts with Typhoon Haitang in a way similar to the binary vortex interaction. The two vortex centers rotate around their system center, which causes looping of Typhoon Haitang.     

Theory and experimental study for sliding isolators with variable curvature

Because a conventional isolation system with constant isolation frequency is usually a long‐period dynamic system, its seismic response is likely to be amplified in earthquakes with strong long‐period wave components, such as near‐fault ground motions. Seismic isolators with variable mechanical properties may provide a promising solution to alleviate this problem. To this end, in this work sliding isolators with variable curvature (SIVC) were studied experimentally. An SIVC isolator is similar to a friction pendulum system (FPS) isolator, except that its sliding surface has variable curvature rather being spherical. As a result, the SIVC's isolation stiffness that is proportional to the curvature becomes a function of the isolator displacement. By appropriately designing the geometry of the sliding surface, the SIVC is able to possess favorable hysteretic behavior. In order to prove the applicability of the SIVC concept, several prototype SIVC isolators, whose sliding surfaces are defined by a sixth‐order polynomial function, were fabricated and tested in this study. A cyclic element test on the prototype SIVC isolators and a shaking table test on an SIVC isolated steel frame were all conducted. The results of both tests have verified that the prototype SIVC isolators do indeed have the hysteretic property of variable stiffness as prescribed by the derived formulas in this study. Moreover, it is also demonstrated that the proposed SIVC is able to effectively reduce the isolator drift in a near‐fault earthquake with strong long‐period components, as compared with that of an FPS system with the same friction coefficient. Copyright © 2011 John Wiley & Sons, Ltd.     

Optimization and capacity expansion of a water distribution system

This paper develops an iterative procedure for capacity expansion studies for water distribution systems. We propose a methodology to analyze an existing water distribution system and identify the potential bottlenecks in the system. Based on the results, capacity expansion alternatives are proposed and evaluated for improving the efficiency of water supply. The methodology includes a network flow based optimization model, four evaluation indices, and a series of evaluation steps. We first use a directed graph to configure the water distribution system into a network. The network flow based model optimizes the water distribution in the system so that different expansion alternatives can be evaluated on a comparable basis. This model lends itself to linear programming (LP) and can be easily solved by a standard LP code. The results from the evaluation tool help to identify the bottlenecks in the water distribution system and provide capacity expansion alternatives. A useful complementary tool for decision making is composed of a series of evaluation steps with the bottleneck findings, capacity expansion alternatives, and the evaluation of results. We apply the proposed methodology to the Tou-Qian River Basin, located in the northern region of Taiwan, to demonstrate its applicability in optimization and capacity expansion studies.     

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].     

Three-dimensional air pollutant modeling in the lower atmosphere

A steady-state, three-dimensional turbulent diffusion equation describing the concentration distribution of an air pollutant from an elevated point source in the lower atmosphere is solved analytically. The same formulation can be used to obtain solutions from line, area or other kinds of sources. The solution is developed for the cases in which the velocity, vertical and lateral diffusivities are given by the power law. The model preserves the beauty of analytical solution without sacrificing much on the accuracy of approximating the velocity and eddy diffusivities. Methods of evaluating the parameters, which are required for the model applications, are discussed. Results indicate that the ratio of the plume width to the plume length increases with decreasing stability and with increasing source height. These consequences are in response to the variations of the size of eddies in the vertical direction.