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.     

A THREE-DIMENSIONAL ELASTIC NESTED-GRID MESO-(β-γ)SCALE ATMOSPHERIC MODEL——PARTI:MODEL DESCRIPTION

A three-dimensional elastic nonhydrostatic mesoscale(β-γ)model with nested-grid is presented.It uses a set of fullequations in terrain-following coordinates as its basic dynamic frame,which is solved with a time-splitting algorithmfor acoustic and gravity waves.The model physical parameterization includes a K-theory subgrid eddy mixing for cloudand free atmosphere,a bulk planetary boundary layer parameterization,and three types of sofisticated cloudmicrophysics schemes with double-parameters for hail-bearing clouds,warm clouds and snowing clouds respectively.The model is designed to be used flexibly for simulations of a variety of meso-and small-scale atmospheric processes,and can be improved as a regional and local operational NWP system in future.     

Ground motion estimation during the Kashmir earthquake of 8th October 2005

In this article, analytical methods have been used to estimate ground motion during the 8 October 2005, Kashmir earthquake. Peak ground acceleration (PGA) values at several stations in the epicentral region have been estimated by empirical analytical source mechanism models. As an alternate analysis, PGA estimates have also been obtained using the stochastic finite fault seismological model. The estimated PGAs are compared with that obtained from damage values. A PGA contour map in the near-source region is provided. It is found that very near to the epicenter, PGA would have reached more than 1 g. It is demonstrated that empirical analytical models can be effectively used to estimate ground motion due to rupture of active faults.     

Income distribution dynamics and cross-region convergence in Europe

This paper presents a continuous version of the model of distribution dynamics to analyse the transition dynamics and implied long-run behaviour of the EU-27 NUTS-2 regions over the period 1995–2003. It departs from previous research in two respects: first, by introducing kernel estimation and three-dimensional stacked conditional density plots as well as highest density regions plots for the visualisation of the transition function, based on Hyndman et al. (J Comput Graph Stat 5(4):315–336, 1996), and second, by combining Getis’ spatial filtering view with kernel estimation to explicitly account for the spatial dimension of the growth process. The results of the analysis indicate a very slow catching-up of the poorest regions with the richer ones, a process of shifting away of a small group of very rich regions, and highlight the importance of geography in understanding regional income distribution dynamics.

Dynamic data integration for structural modeling: model screening approach using a distance-based model parameterization

This paper proposes a novel history-matching method where reservoir structure is inverted from dynamic fluid flow response. The proposed workflow consists of searching for models that match production history from a large set of prior structural model realizations. This prior set represents the reservoir structural uncertainty because of interpretation uncertainty on seismic sections. To make such a search effective, we introduce a parameter space defined with a “similarity distance” for accommodating this large set of realizations. The inverse solutions are found using a stochastic search method. Realistic reservoir examples are presented to prove the applicability of the proposed method.     

SOME NEW UNDERSTANDINGS OF LAND-SURFACE PROCESSES IN ARID AREA FROM THE HEIFE*

The survey for the HEIFE(Atmosphere-Land Surface Processes Experiment at Heihe River Basin,Western China) is given in the paper.The following basic subjects for land-surface processes in arid areas are studied:(1) the general characteristics of the energy budget on ground surface in arid areas;(2) the parameterization of the land surface processes;(3) the interaction between oasis and its desert circumstances,a special phenomenon in arid areas.The analysis shows that the sensible heat flux in the surface energy budget is in the majority,and the latent heat flux may be neglected.The influence of atmospheric stratification stability on the turbulent transfer of energy and substance must be considered in parameterization of land surface processes in arid areas.The "cold island effect" phenomenon in oasis and the "humidity inversion" phenomenon in desert near oasis are the result of the interaction between them.The results would improve the understanding of land surface processes in arid areas.     

Combination of Dependent Realizations Within the Gradual Deformation Method

Gradual deformation is a parameterization method that reduces considerably the unknown parameter space of stochastic models. This method can be used in an iterative optimization procedure for constraining stochastic simulations to data that are complex, nonanalytical functions of the simulated variables. This method is based on the fact that linear combinations of multi-Gaussian random functions remain multi-Gaussian random functions. During the past few years, we developed the gradual deformation method by combining independent realizations. This paper investigates another alternative: the combination of dependent realizations. One of our motivations for combining dependent realizations was to improve the numerical stability of the gradual deformation method. Because of limitations both in the size of simulation grids and in the precision of simulation algorithms, numerical realizations of a stochastic model are never perfectly independent. It was shown that the accumulation of very small dependence between realizations might result in significant structural drift from the initial stochastic model. From the combination of random functions whose covariance and cross-covariance are proportional to each other, we derived a new formulation of the gradual deformation method that can explicitly take into account the numerical dependence between realizations. This new formulation allows us to reduce the structural deterioration during the iterative optimization. The problem of combining dependent realizations also arises when deforming conditional realizations of a stochastic model. As opposed to the combination of independent realizations, combining conditional realizations avoids the additional conditioning step during the optimization process. However, this procedure is limited to global deformations with fixed structural parameters.     

Coupled inverse modelling of groundwater flow and mass transport and the worth of concentration data

This paper presents the extension of the self-calibrating method to the coupled inverse modelling of groundwater flow and mass transport. The method generates equally likely solutions to the inverse problem that display the variability as observed in the field and are not affected by a linearisation of the state equations. Conditioning to the state variables is measured by an objective function including, among others, the mismatch between the simulated and measured concentrations. Conditioning is achieved by minimising the objective function by gradient-based methods. The gradient contains the partial derivatives of the objective function with respect to: log conductivities, log storativities, prescribed heads at boundaries, retardation coefficients and mass sources. The derivatives of the objective function with respect to log conductivity are the most cumbersome and need the most CPU-time to be evaluated. For this reason, to compute this derivative only advective transport is considered. The gradient is calculated by the adjoint-state method. The method is demonstrated in a controlled, synthetic study, in which the worth of concentration data is analysed. It is shown that concentration data are essential to improve transport predictions and also help to improve aquifer characterisation and flow predictions, especially in the upstream part of the aquifer, even in the case that a considerable amount of other experimental data like conductivities and heads are available. Besides, conditioning to concentration data reduces the ensemble variances of estimated transmissivity, hydraulic head and concentration.     

Adaptive Multiscale Permeability Estimation

With multiscale permeability estimation one does not select parameterization prior to the estimation. Instead, one performs a hierarchical search for the right parameterization while solving a sequence of estimation problems with an increasing parameterization dimension. In some previous works on the subject, the same refinement is applied all over the porous medium. This may lead to over-parameterization, and subsequently, to unrealistic permeability estimates and excessive computational work. With adaptive multiscale permeability estimation, the new parameterization at an arbitrary stage in the estimation sequence is such that new degrees of freedom are not necessarily introduced all over the porous medium. The aim is to introduce new degrees of freedom only where it is warranted by the data. In this paper, we introduce a novel adaptive multiscale estimation. The approach is used to estimate absolute permeability from two-phase pressure data in several numerical examples.     

荒漠戈壁下垫面表面动量和感热湍流通量参数化研究

用合理筛选以后的野外观测资料，研究了荒漠戈壁地表湍流通量参数化的问题。首先，分析了Monin-obukhov相似函数的特征，并拟台出了其经验公式。结果表明，风速和温度相似性函数随稳定度参数的变化曲线与典型经验曲线差异较小，并且在经验曲线分布范围以内，但中性时的值有所不同。同时，还用该资料给出了动量和标量粗糙度(感热粗糙度)长度的平均值及其标量粗糙度随摩擦速度的变化关系。发现标量粗糙度的平均值大约比动量粗糙度的小一个量级，并且随摩擦速度的增大而减小，但明显比其理论预测值要大。