On the modelling of sand bedforms using the semivariogram

This study shows the usefulness of the semivariogram for modelling sand ripples created by water flows of varied flow intensity. A combination of two mathematical functions is fitted to each sample semivariogram, that is an exponential (or stochastic) component and a periodic component. The parameters of each of these components have direct physical meaning. A non-dimensional ratio combining the two parameters of the exponential model is interpreted as a regularity index (which increases with the degree of regularity of bedform arrangement). This regularity index is inversely related to the Froude number of the flow. The non-dimensional wavelength, estimated from the dominant periodic function, is also inversely and closely related to the Froude number. The wave height, accurately estimated from properties of the two fitted components, is a direct function of flow velocity and is also proportional to the standard deviation of bed elevations. The bedform shape introduces a considerable discrepancy between the generally assumed normal frequency distribution and the empirical distributions of bed height. The series of bed elevations are generally characterized by a mixture of normal distributions having the same variance but different means. The calculation of a covariance assuming a constant and single mean (as in spectral analysis) can therefore be misleading and the problem may be avoided by using the semivariogram.     

Ground water contaminant transport by nondivergence-free, unsteady and nonstationary velocity fields

Pore flow velocity is assumed to be a nondivergence-free, unsteady, and nonstationary random function of space and time for ground water contaminant transport in a heterogeneous medium. The laboratory-scale stochastic contaminant transport equation is up scaled to field scale by taking the ensemble average of the equation by using the cumulant expansion method. A new velocity correction, which is a function of mean pore flow velocity divergence, is obtained due to strict second order cumulant expansion (without omitting any term after the expansion). The field scale transport equations under the divergence-free pore flow velocity field assumption are also derived by simplifying the nondivergence-free field scale equation. The significance of the new velocity correction term is investigated on a two dimensional transport problem driven by a density dependent flow.     

A stochastic model of surface contaminant releases to support assessment of site contamination at a former industrial site

An industrial site is usually contaminated by accidental (and occasionally intentional) releases of pollutants to the environment from various operations carried out on that site. Consequently, the pattern of contamination created during the life of the site depends in part, at least, on the pattern of operations. Thus, the assessment of the pattern of contamination over the site should be improved: if it is possible to identify the pattern of operations on the site, the duration of the different activities and the perceived likelihood of releases from the different operations. A stochastic model has been developed that can be used to simulate alternative realizations of contaminant releases (duration, extent and timing). The model employs release zones associated with particular activities or groups of activities on the site and the areas of each of the zones may be independent or overlapping. The period of activity in each zone is obtained from the site records, while the likelihood and extent of contamination in each zone is inferred from an analysis of the contamination data obtained by point sampling. The form of the model, the method of inference of the model parameter values from the site data and the application of the model to the study site are presented. The release model has been developed as part of a suite of stochastic models for site ground contamination analysis. The stochastic soil and transport models and the application of the integrated modelling system are described in separate papers.     

随机Petri网在地震应急协同能力定量评价与动态分析中的应用

地震应急是一个复杂动态的过程,需要各部门协同配合方能高效开展应急工作。本文通过调研分析历史地震应急处置案例,提出了Ⅰ、Ⅱ级应急响应下多主体地震应急协同的一般流程,构建了相应的随机Petri网模型,并基于Petri网可能出现的状态集同构马尔科夫链,在计算各应急状态稳定概率的基础上,定量评价应急协同能力。同时,将应急过程中利用率高的变迁所对应的应急行为,作为应急处置的关键环节。通过调整各关键环节的应急速率,进一步对应急协同能力进行动态分析,进而提出有效提高应急协同联动能力的相关建议,为科学开展地震应急处置工作提供支持。     

Steady- and transient-state inversion in hydrogeology by successive flux estimation

A calibration method to solve the groundwater inverse problem under steady- and transient-state conditions is presented. The method compares kriged and numerical head field gradients to modify hydraulic conductivity without the use of non-linear optimization techniques. The process is repeated iteratively until a close match with piezometric data is reached. The approach includes a damping factor to avoid divergence and oscillation of the solution in areas of low hydraulic gradient and a weighting factor to account for temporal head variation in transient simulations. The efficiency of the method in terms of computing time and calibration results is demonstrated with a synthetic field. It is shown that the proposed method provides parameter fields that reproduce both hydraulic conductivity and piezometric data in few forward model solutions. Stochastic numerical experiments are conducted to evaluate the sensitivity of the method to the damping function and to the head field estimation errors.     

Planning hydroelectric resources with recourse-based multistage interval-stochastic programming

Optimization models play an important role in long-term hydroelectric resources planning. The effectiveness of an optimization model, however, depends on its capability of dealing with uncertainties. This study presents a multistage interval-stochastic programming model for long-term hydropower planning, in which uncertainties are reflected as randomness and intervals. The model is developed based on interval programming technique and recourse-based multistage stochastic programming and using the expected value of long-term hydroelectric profit as the objective function. A solution method of the developed model is also presented, which is based on a decomposition method by partitioning the multistage interval-stochastic program into two-stage stochastic programming sub-problems in each scenario-tree node. A hypothetical case study is used to demonstrate the developed model and its solution method. Modeling results demonstrates the computationally effectiveness of the solution method and reveal the applicability of the developed model for long term planning of hydroelectric resources.     

Geophysical flows under location uncertainty,Part I Random transport and general models

A stochastic flow representation is considered with the Eulerian velocity decomposed between a smooth large scale component and a rough small-scale turbulent component. The latter is specified as a random field uncorrelated in time. Subsequently, the material derivative is modified and leads to a stochastic version of the material derivative to include a drift correction, an inhomogeneous and anisotropic diffusion, and a multiplicative noise. As derived, this stochastic transport exhibits a remarkable energy conservation property for any realizations. As demonstrated, this pivotal operator further provides elegant means to derive stochastic formulations of classical representations of geophysical flow dynamics.     

Geophysical flows under location uncertainty,Part II Quasi-geostrophy and efficient ensemble spreading

Models under location uncertainty are derived assuming that a component of the velocity is uncorrelated in time. The material derivative is accordingly modified to include an advection correction, inhomogeneous and anisotropic diffusion terms and a multiplicative noise contribution. In this paper, simplified geophysical dynamics are derived from a Boussinesq model under location uncertainty. Invoking usual scaling approximations and a moderate influence of the subgrid terms, stochastic formulations are obtained for the stratified Quasi-Geostrophy and the Surface Quasi-Geostrophy models. Based on numerical simulations, benefits of the proposed stochastic formalism are demonstrated. A single realization of models under location uncertainty can restore small-scale structures. An ensemble of realizations further helps to assess model error prediction and outperforms perturbed deterministic models by one order of magnitude. Such a high uncertainty quantification skill is of primary interests for assimilation ensemble methods. MATLAB^® code examples are available online.     

A modelling framework for evaluation of the hydrological impacts of nature‐based approaches to flood risk management,with application to in‐channel interventions across a 29‐km2 scale catchment in the United Kingdom

Nature‐based approaches to flood risk management are increasing in popularity. Evidence for the effectiveness at the catchment scale of such spatially distributed upstream measures is inconclusive. However, it also remains an open question whether, under certain conditions, the individual impacts of a collection of flood mitigation interventions could combine to produce a detrimental effect on runoff response. A modelling framework is presented for evaluation of the impacts of hillslope and in‐channel natural flood management interventions. It couples an existing semidistributed hydrological model with a new, spatially explicit, hydraulic channel network routing model. The model is applied to assess a potential flood mitigation scheme in an agricultural catchment in North Yorkshire, United Kingdom, comprising various configurations of a single variety of in‐channel feature. The hydrological model is used to generate subsurface and surface fluxes for a flood event in 2012. The network routing model is then applied to evaluate the response to the addition of up to 59 features. Additional channel and floodplain storage of approximately 70,000 m³ is seen with a reduction of around 11% in peak discharge. Although this might be sufficient to reduce flooding in moderate events, it is inadequate to prevent flooding in the double‐peaked storm of the magnitude that caused damage within the catchment in 2012. Some strategies using features specific to this catchment are suggested in order to improve the attenuation that could be achieved by applying a nature‐based approach.     

1D elastic full‐waveform inversion and uncertainty estimation by means of a hybrid genetic algorithm–Gibbs sampler approach

Stochastic optimization methods, such as genetic algorithms, search for the global minimum of the misfit function within a given parameter range and do not require any calculation of the gradients of the misfit surfaces. More importantly, these methods collect a series of models and associated likelihoods that can be used to estimate the posterior probability distribution. However, because genetic algorithms are not a Markov chain Monte Carlo method, the direct use of the genetic‐algorithm‐sampled models and their associated likelihoods produce a biased estimation of the posterior probability distribution. In contrast, Markov chain Monte Carlo methods, such as the Metropolis–Hastings and Gibbs sampler, provide accurate posterior probability distributions but at considerable computational cost. In this paper, we use a hybrid method that combines the speed of a genetic algorithm to find an optimal solution and the accuracy of a Gibbs sampler to obtain a reliable estimation of the posterior probability distributions. First, we test this method on an analytical function and show that the genetic algorithm method cannot recover the true probability distributions and that it tends to underestimate the true uncertainties. Conversely, combining the genetic algorithm optimization with a Gibbs sampler step enables us to recover the true posterior probability distributions. Then, we demonstrate the applicability of this hybrid method by performing one‐dimensional elastic full‐waveform inversions on synthetic and field data. We also discuss how an appropriate genetic algorithm implementation is essential to attenuate the “genetic drift” effect and to maximize the exploration of the model space. In fact, a wide and efficient exploration of the model space is important not only to avoid entrapment in local minima during the genetic algorithm optimization but also to ensure a reliable estimation of the posterior probability distributions in the subsequent Gibbs sampler step.