Spatial moments for colloid-enhanced radionuclide transport in heterogeneous aquifers

We consider colloid facilitated radionuclide transport by steady groundwater flow in a heterogeneous porous formation. Radionuclide binding on colloids and soil-matrix is assumed to be kinetically/equilibrium controlled. All reactive parameters are regarded as uniform, whereas the hydraulic log-conductivity is modelled as a stationary random space function (RSF). Colloid-enhanced radionuclide transport is studied by means of spatial moments pertaining to both the dissolved and colloid-bounded concentration. The general expressions of spatial moments for a colloid-bounded plume are presented for the first time, and are discussed in order to show the combined impact of sorption processes as well as aquifer heterogeneity upon the plume migration. For the general case, spatial moments are defined by the aid of two characteristic reaction functions which cannot be expressed analytically. By adopting the approximation for the longitudinal fluid trajectory covariance valid for a flow parallel to the formation bedding suggested by Dagan and Cvetkovic [Dagan G, Cvetkovic V. Spatial Moments of Kinetically Sorbing Plume in a Heterogeneous Aquifers. Water Resour Res 1993;29:4053], we obtain closed form solutions.     

Test application of Bayesian Programming: Adaptive water quality management under uncertainty

A new method, Bayesian Programming (BP), developed by Harrison [Harrison KW. Multi-stage decision-making under uncertainty and stochasticity: Bayesian Programming. Adv Water Resour, submitted for publication] is tested on a case study involving optimal adaptive management of a river basin. The case study considers anew the process of permitting pulp mills on the Athabasca River in Alberta, Canada. The problem has characteristics common to many environmental management problems. There is uncertainty in the water quality response to pollutant loadings that will not be completely resolved with monitoring and the resolution of this uncertainty is impeded by the stochastic behavior of the water quality system. A two-stage adaptive management process is optimized with BP. Based on monitoring data collected after implementation of the first-stage decision, the uncertainties are updated prior to the second decision stage using Bayesian analysis. The worth of this two-stage adaptive management approach to this problem and the worth of monitoring are evaluated. Conclusions are drawn on the general practicality of BP for adaptive management. Potential strategies are outlined for extending the BP approach to secure further benefits of adaptive management.     

Effective dispersion in a chemically heterogeneous medium under temporally fluctuating flow conditions

We investigate effective solute transport in a chemically heterogeneous medium subject to temporal fluctuations of the flow conditions. Focusing on spatial variations in the equilibrium adsorption properties, the corresponding fluctuating retardation factor is modeled as a stationary random space function. The temporal variability of the flow is represented by a stationary temporal random process. Solute spreading is quantified by effective dispersion coefficients, which are derived from the ensemble average of the second centered moments of the normalized solute distribution in a single disorder realization. Using first-order expansions in the variances of the respective random fields, we derive explicit compact expressions for the time behavior of the disorder induced contributions to the effective dispersion coefficients. Focusing on the contributions due to chemical heterogeneity and temporal fluctuations, we find enhanced transverse spreading characterized by a transverse effective dispersion coefficient that, in contrast to transport in steady flow fields, evolves to a disorder-induced macroscopic value (i.e., independent of local dispersion). At the same time, the asymptotic longitudinal dispersion coefficient can decrease. Under certain conditions the contribution to the longitudinal effective dispersion coefficient shows superdiffusive behavior, similar to that observed for transport in s stratified porous medium, before it decreases to its asymptotic value. The presented compact and easy to use expressions for the longitudinal and transverse effective dispersion coefficients can be used for the quantification of effective spreading and mixing in the context of the groundwater remediation based on hydraulic manipulation and for the effective modeling of reactive transport in heterogeneous media in general.     

Analytical representation of phase characteristics for source time function modeled by stochastic impulse train

In order to discuss the relationship between the lower and higher frequency components of earthquake source spectra, we deal with impulse train model as source time function of earthquake, because spectral characteristics of source time function depend on occurrence times of impulse function which corresponds to small extent on the fault. Then, the spectral characteristics of source time function are obtained analytically and numerically from the stochastic viewpoints: namely, on one hand, the trend of impulse train dominates the frequency characteristics in low frequency range, and on the other hand, the fluctuation from the trend settles high frequency range. Furthermore, it is shown that the spectral properties of source time function can be determined using only two parameters which are number of impulses n and the probability density function of occurrence time of impulses f_T(t).     

Assessment of prediction performances of stochastic models: Monthly groundwater level prediction in Southern Italy

Stochastic modelling of hydrological time series with insufficient length and data gaps is a serious challenge since these problems significantly affect the reliability of statistical models predicting and forecasting skills. In this paper, we proposed a method for searching the seasonal autoregressive integrated moving average(SARIMA) model parameters to predict the behavior of groundwater time series affected by the issues mentioned. Based on the analysis of statistical indices, 8 stations among 44 available within the Campania region(Italy) have been selected as the highest quality measurements. Different SARIMA models, with different autoregressive, moving average and differentiation orders had been used.By reviewing the criteria used to determine the consistency and goodness-of-fit of the model, it is revealed that the model with specific combination of parameters, SARIMA(0,1,3)(0,1,2) _(12), has a high R~2 value,larger than 92%, for each of the 8 selected stations. The same model has also good performances for what concern the forecasting skills, with an average NSE of about 96%. Therefore, this study has the potential to provide a new horizon for the simulation and reconstruction of groundwater time series within the investigated area.     

Comparison of sparse‐grid geometric and random sampling methods in nonlinear inverse solution uncertainty estimation

A new uncertainty estimation method, which we recently introduced in the literature, allows for the comprehensive search of model posterior space while maintaining a high degree of computational efficiency. The method starts with an optimal solution to an inverse problem, performs a parameter reduction step and then searches the resulting feasible model space using prior parameter bounds and sparse‐grid polynomial interpolation methods. After misfit rejection, the resulting model ensemble represents the equivalent model space and can be used to estimate inverse solution uncertainty. While parameter reduction introduces a posterior bias, it also allows for scaling this method to higher dimensional problems. The use of Smolyak sparse‐grid interpolation also dramatically increases sampling efficiency for large stochastic dimensions. Unlike Bayesian inference, which treats the posterior sampling problem as a random process, this geometric sampling method exploits the structure and smoothness in posterior distributions by solving a polynomial interpolation problem and then resampling from the resulting interpolant. The two questions we address in this paper are 1) whether our results are generally compatible with established Bayesian inference methods and 2) how does our method compare in terms of posterior sampling efficiency. We accomplish this by comparing our method for two electromagnetic problems from the literature with two commonly used Bayesian sampling schemes: Gibbs’ and Metropolis‐Hastings. While both the sparse‐grid and Bayesian samplers produce compatible results, in both examples, the sparse‐grid approach has a much higher sampling efficiency, requiring an order of magnitude fewer samples, suggesting that sparse‐grid methods can significantly improve the tractability of inference solutions for problems in high dimensions or with more costly forward physics.     

Multi-objective stochastic-structural-optimization of shape-memory-alloy assisted pure-friction bearing for isolating building against random earthquakes

The optimal stochastic performance of pure friction system supplemented with SMA-restrainer (SMA-PF) is presented based on a framework of multi-objective optimization. The evaluation of system response for this is based on nonlinear random vibration analysis. The optimizing design variables are based on two mutually conflicting objectives, involving maximizing the isolation efficiency as well as isolator displacement. The proposed optimal design, thus, not only maximizes the isolation efficiency but also impose due consideration to the bearing displacement. The optimal bearing is shown to substantially reduce the bearing displacement with nominal sacrifice in isolation efficiency. Comparison of the multi-objective Pareto fronts reveals much facilitated trade-off among the mutually conflicting objectives in SMA-PF than in PF system. The viability of the optimal performance is further verified under recorded ground motions, which is observed to be in parity to the stochastic response behavior. The reduction in the residual bearing displacement is also observed.     

Several effects of baroclinic currents on the three‐dimensional propagation of inertial‐internal waves†

A ray theory is applied to the problem of three‐dimensional propagation of inertial‐internal waves in the presence of a mean baroclinic current which does not vary in the downstream coordinate. As time increases, the Doppler‐shifted wave frequency, or intrinsic frequency, tends to a limiting value determined by the horizontal and vertical variations of the mean current and density fields. The limiting value of the intrinsic frequency determines critical surfaces where energy is transferred to the mean motion. Also, the group velocity tends to the mean current velocity, and the phase velocity tends to be oriented towards or away from the core of the mean current, depending upon whether the wave is either initially propagating with a wave number component antiparallel or parallel to the mean current.     

晋祠泉域汾河干流古交段河道渗漏分析研究

晋祠泉域汾河干流古交段属山区峡谷,河谷大部分河段寒武、奥陶系碳酸盐岩类可溶性岩层裸露,河道渗漏量大。根据试验断面测流数据,建立了不同渗漏段上游断面流量及渗漏系数关系模型,分析各渗漏段渗漏规律,推算渗漏量,为晋祠泉水复流工程汾河干流古交渗漏段补水方案提供参考。     

Automated statistical matching of multiple tephra records exemplified using five long maar sequences younger than 75 ka,Auckland, New Zealand

Detailed tephrochronologies are built to underpin probabilistic volcanic hazard forecasting, and to understand the dynamics and history of diverse geomorphic, climatic, soil-forming and environmental processes. Complicating factors include highly variable tephra distribution over time; difficulty in correlating tephras from site to site based on physical and chemical properties; and uncertain age determinations. Multiple sites permit construction of more accurate composite tephra records, but correctly merging individual site records by recognizing common events and site-specific gaps is complex. We present an automated procedure for matching tephra sequences between multiple deposition sites using stochastic local optimization techniques. If individual tephra age determinations are not significantly different between sites, they are matched and a more precise age is assigned. Known stratigraphy and mineralogical or geochemical compositions are used to constrain tephra matches. We apply this method to match tephra records from five long sediment cores (≤ 75 cal ka BP) in Auckland, New Zealand. Sediments at these sites preserve basaltic tephras from local eruptions of the Auckland Volcanic Field as well as distal rhyolitic and andesitic tephras from Okataina, Taupo, Egmont, Tongariro, and Tuhua (Mayor Island) volcanic centers. The new correlated record compiled is statistically more likely than previously published arrangements from this area.