Stochastic modelling of groundwater flow and solute transport in aquifers

This paper presents an introductory overview of recently developed stochastic theories for tackling spatial variability problems in predicting groundwater flow and solute transport. Advantages and limitations of the theories are discussed. Lastly, strategies based on the stochastic approaches to predict solute transport in aquifers are recommended.     

Effect of spatial variation characteristics on contouring of design storm depth

The ordinary kriging method, a geostatistical interpolation technique, was applied for developing contour maps of design storm depth in northern Taiwan using intensity–duration–frequency (IDF) data. Results of variogram modelling on design storm depths indicate that the design storms can be categorized into two distinct storm types: (i) storms of short duration and high spatial variation and (ii) storms of long duration and less spatial variation. For storms of the first category, the influence range of rainfall depth decreases when the recurrence interval increases, owing to the increasing degree of their spatial independence. However, for storms of the second category, the influence range of rainfall depth does not change significantly and has an average of approximately 72 km. For very extreme events, such as events of short duration and long recurrence interval, we do not recommend usage of the established design storm contours, because most of the interstation distances exceed the influence ranges. Our study concludes that the influence range of the design storm depth is dependent on the design duration and recurrence interval and is a key factor in developing design storm contours. Copyright © 2003 John Wiley & Sons, Ltd.     

Crustal Structures of the Northernmost South China Sea: Seismic Reflection and Gravity Modeling

The South China Sea (SCS) is a marginal sea off shore Southeast Asia. Based on magnetic study, oceanic crust has been suggested in the northernmost SCS. However, the crustal structure of the northernmost SCS was poorly known. To elaborate the crustal structures in the northernmost SCS and off southwest Taiwan, we have analyzed 20 multi-channel seismic profiles of the region. We have also performed gravity modeling to understand the Moho depth variation. The volcanic basement deepens southeastwards while the Moho depth shoals southeastwards. Except for the continental margin, the northernmost SCS can be divided into three tectonic regions: the disturbed and undisturbed oceanic crust (8–12 km thick) in the southwest, a trapped oceanic crust (8 km thick) between the Luzon-Ryukyu Transform Plate Boundary (LRTPB) and Formosa Canyon, and the area to the north of the Formosa Canyon which has the thickest sediments. Instead of faulting, the sediments across the LRTPB have only displayed differential subsidence offset of about 0.5–1 s in the northeast side, indicating that the LRTPB is no longer active. The gravity modeling has shown a relatively thin crust beneath the LRTPB, demonstrating the sheared zone character along the LRTPB. However, probably because of post-spreading volcanism, only the transtension-shearing phenomenon of volcanic basement in the northwest and southeast ends of the LRTPB can be observed. These two basement-fractured sites coincide with low gravity anomalies. Intensive erosion has prevailed over the whole channel of the Formosa Canyon.     

Regionalization of unit hydrograph parameters: 1. Comparison of regression analysis techniques

Hydrologic regionalization is a useful tool that allows for the transfer of hydrological information from gaged sites to ungaged sites. This study developed regional regression equations that relate the two parameters in Nash's IUH model to the basin characteristics for 42 major watersheds in Taiwan. In the process of developing the regional equations, different regression procedures including the conventional univariate regression, multivariate regression, and seemingly unrelated regression were used. Multivariate regression and seeming unrelated regression were applied because there exists a rather strong correlation between the Nash's IUH parameters. Furthermore, a validation study was conducted to examine the predictability of regional equations derived by different regression procedures. The study indicates that hydrologic regionalization involving several dependent variables should consider their correlations in the process of establishing the regional equations. The consideration of such correlation will enhance the predictability of resulting regional equations as compared with the ones from the conventional univariate regression procedure.     

Regionalization of unit hydrograph Parameters: 2. Uncertainty analysis

Hydrologic model parameters obtained from regional regression equations are subject to uncertainty. Consequently, hydrologic model outputs based on the stochastic parameters are random. This paper presents a systematic analysis of uncertainty associated with the two parameters, N and K, in Nash's IUH model from different regional regression equations. The uncertainty features associated with N and K are further incorporated to assess the uncertainty of the resulting IUH. Numerical results indicate that uncertainty of N and K from the regional regression equations are too significant to be ignored.     

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.     

The attenuation of acoustic-gravity waves in a slightly dissipative atmosphere

This paper is concerned with computation of the attenuation coefficient of internal acoustic-gravity waves in a slightly dissipative horizontally stratified atmosphere. Two models are generally used in deriving this attenuation coefficient. In one model, the nonlinear hydrodynamic equations are analyzed by using a Stokes expansion and the WKB solutions to the linearized perturbations are sought by using the coupled mode formulation. In the second model, the attenuation is viewed as the dissipation of pseudoenergy. We show in this paper that in a slightly dissipative atmosphere, these two models give identical results as far as computation of the attenuation coefficient is concerned, although in a highly dissipative atmosphere the results are known to be different.     

Synoptic and mesoscale study of a severe convective outbreak with the nonhydrostatic Global Environmental Multiscale (GEM) model

Summary ?A nonhydrostatic 4-km version of the Global Environmental Multiscale (GEM) model, with detailed microphysics included, was used to forecast the initiation, development, and structure of a tornado-producing supercell storm that occurred near Pine Lake (Alberta, Canada) on 15 July 2000. Examination of observations and comparison with conceptual models indicate that this storm is a good example of supercell storms that regularly produce summertime severe weather over Alberta. It was found that the high-resolution model was able to reproduce the early initiation of convective activity along the Rocky Mountains foothills, as well as the rapid northeastward propagation towards the Pine Lake area and the subsequent intensification into a supercell storm. The general structures of the forecasted convective system correspond well with conceptual representations of such events. Overall, this high-resolution forecast of the Pine Lake supercell storm was a significant improvement over the current operational version of the GEM model (24 km), which was not able to intensify the foothills’ convection into a supercell storm. Finally, it was found that the nonhydrostatic version of the model produces better trajectory and propagation speed of the convective system, as compared with the hydrostatic one. Received March 20, 2001; revised August 24, 2001     

A solution for simultaneous turbulent heat and vapor transfer between a water surface and the atmosphere

Interaction between sensible heat and water vapor diffusion in the lower atmosphere leads to the necessity of solving two simultaneous turbulent diffusion equations. This solution is obtained by the construction of Green's function which when incorporated in the boundary conditions produces two integral equations. These are solved by transformation into two algebraic equations by means of the Laplace Transformation. The results show how for a simple steady-state case, sensible heat and water vapor transfer and also the water surface temperature depend on the meteorological conditions and the rate of change of energy content of the water body. Due to advection, the water surface temperature and the turbulent fluxes vary in the downwind direction. However, for practical calculations of the mean evaporation or heat transfer, the error introduced by the use of an average temperature is usually quite small and negligible.