Using stochastic state‐space modelling to specify and reduce hydrograph error

A Bayesian post‐processor is used to generate a representation of the likely hydrograph forecast flow error distribution using raingauge and radar input to a stochastic catchment model and its deterministic equivalent. A hydrograph ensemble is so constructed. Experiments are analysed using the model applied to the River Croal in north‐west England. It is found that for rainfall input to the model having errors less than 3mm h^?1, corresponding to about a 15% error in peak flow, the stochastic model outperforms the deterministic model. The range of hydrographs associated with the different model simulations and the measured hydrographs are compared. The significant improvement possible using a stochastic approach is demonstrated for a specific case study, although the mean hydrograph derived using the stochastic model has an error range associated with it. Copyright © 2007 John Wiley & Sons, Ltd.     

Two methods for pore network of porous media

Two approaches of generating pore networks of porous media are presented to capture the pore fabric. The first methodology extracted pore structure from a computer simulated packing of spheres. The modified Delaunay tessellation was used to describe the porous media, and modified Nelder–Mead method in conjunction with three pore‐merging algorithms was used to generate the pore size and coordination number distributions of the randomly packed spheres. The Biconical Abscissa Asymmetric CONcentric bond was used to describe the connection between two adjacent voids. This algorithm was validated by predicting pore structure of a cubic array of spheres of equal radius with known pore sizes, throat sizes and coordination number distributions. The predicted distributions of pore structure agreed well with the measured. Then, the algorithm was used to predict pore structure and permeability of randomly packed spherical particles, and predicted permeability values were compared with published experimental data. The results showed that the predicted permeability values were in good agreement with those measured, confirming the proposed algorithm can capture the main flow paths of packed beds. The second methodology generated an equivalent pore network of porous media, of which the centers of voids were located in a regular lattice with constant pore center distance. However, this network allowed for matching both main geometrical and topological characteristics of the porous media. A comparison of the two approaches suggested that the second approach can also be used as a predictive tool to quantitatively study the microscopic properties of flow through porous media. Copyright © 2012 John Wiley & Sons, Ltd.     

Numerical study of soil heterogeneity effects on contaminant transport in unsaturated soil (model development and validation)

The movement of chemicals through soil to groundwater is a major cause of degradation of water resources. In many cases, serious human and stock health implications are associated with this form of pollution. The study of the effects of different factors involved in transport phenomena can provide valuable information to find the best remediation approaches. Numerical models are increasingly being used for predicting or analyzing solute transport processes in soils and groundwater. This article presents the development of a stochastic finite element model for the simulation of contaminant transport through soils with the main focus being on the incorporation of the effects of soil heterogeneity in the model. The governing equations of contaminant transport are presented. The mathematical framework and the numerical implementation of the model are described. The comparison of the results obtained from the developed stochastic model with those obtained from a deterministic method and some experimental results shows that the stochastic model is capable of predicting the transport of solutes in unsaturated soil with higher accuracy than deterministic one. The importance of the consideration of the effects of soil heterogeneity on contaminant fate is highlighted through a sensitivity analysis regarding the variance of saturated hydraulic conductivity as an index of soil heterogeneity. Copyright © 2011 John Wiley & Sons, Ltd.     

Variability of volume strain in bounded heterogeneous media

The deformation of the solid matrix affects the fluid pore pressure and flow by altering the pore volume. Such interaction in turn affects the storage of groundwater in the void space. Obviously, this subject is of interest in groundwater hydrology. This paper describes an investigation of the effect of aquifer heterogeneity on the variability of the fluid pressure head and solid's volume strain, where the assumption of a constant vertical total stress leads to a relatively simple relationship between changes in solid's volume strain and fluid pressure head. To solve the problem analytically, focus is placed on the one‐dimensional models. It is found from our closed‐form solutions that the variance and correlation length of the log hydraulic conductivity are important in increasing the variability of pressure head and solid's volume strain. It is hoped that our findings will provide a basic framework for understanding and quantifying field‐scale volume strain processes and be useful in stimulating further research in this area. Copyright © 2011 John Wiley & Sons, Ltd.     

A theory of pressure sensor performance in snow

A theory of pressure sensor response in snow is derived and used to examine the sources of measurement errors in snow water equivalent (SWE) pressure sensors. Measurement errors in SWE are caused by differences in the compressibility of the pressure sensor and the adjacent snow layer, which produces a shear stress along the perimeter of the sensor. When the temperature at the base of the snow cover equals 0 °C, differences in the snowmelt rate between the snow–SWE sensor interface and the adjacent snow–soil interface may also produce a shear stress along the sensor's perimeter. This shear stress perturbs the pressure field over the sensor, producing SWE measurement errors. Snow creep acts to reduce shear stresses along the SWE sensor's perimeter at a rate that is inversely proportional to the snow viscosity. For sustained periods of differential snowmelt, a difference in the mass of snow over the sensor compared with the surrounding soil will develop, producing additional permanent errors in SWE measurements. The theory indicates that SWE pressure sensor performance can be improved by designing a sensor with a high Young's modulus (low compressibility), low aspect ratio, large diameter and thermal properties that match those of the surrounding soil. Simulations of SWE pressure sensor errors using the theory are in close agreement with observed errors and may provide a means to correct historical SWE measurements for use in hydrological hindcast or climate studies. Published in 2003 by John Wiley & Sons, Ltd.     

Forced secondary resonances at the 3 : 1 commensurability

For the 3 : 1 Jovian resonance problem, the time scales of the two degrees of freedom of the resonant Hamiltonian are well-separated [5]. With the adiabatic approximation, the solution for the fast oscillations can be found in terms of the slowly varying variables. Thus the rapidly oscillating terms in the slow oscillation equations can be treated as forced terms. We refer to the resonance between the forcing and intrinsic frequencies as a forced secondary one in this paper. We discuss the forced secondary resonances in asteroidal motion at the 3 : 1 commensurability by using Wisdom's method. The results show that the orbits situated originally near the resonance will leave the neighbourhood of resonance and tend to the separatrices and critical points for different energies, respectively. We have not found any stochastic web as expected in this case. Moreover, we study the problem of validity on the approximation of a system.The Project Supported by the National Natural Science Foundation of China.     

大型高精度GNSS基线向量网并行抗差估计

针对大型GNSS基线向量网的特点,在改进的相关观测抗差估计RECO方案的基础上采用并行计算技术进行相关抗差估计的并行计算(简称"并行抗差估计"),并给出了可行的解算步骤。通过算例分析,验证了大型GNSS基线向量网的并行相关抗差估计,不仅有效抑制了观测异常对参数估值的影响,而且显著提高了计算效率。     

Radio‐tracking gravel particles in a large braided river in New Zealand: a field test of the stochastic theory of bed load transport proposed by Einstein

Hans A. Einstein initiated a probabilistic approach to modelling sediment transport in rivers. His formulae were based on theory and were stimulated by laboratory investigations. The theory assumes that bed load movement occurs in individual steps of rolling, sliding or saltation and rest periods. So far very few attempts have been made to measure stochastic elements in nature. For the first time this paper presents results of radio‐tracing the travel path of individual particles in a large braided gravel bed river: the Waimakariri River of New Zealand. As proposed by Einstein, it was found that rest periods can be modelled by an exponential distribution, but particle step lengths are better represented by a gamma distribution. Einstein assumed an average travel distance of 100 grain‐diameters for any bed load particle between consecutive points of deposition, but larger values of 6·7 m or 150 grain‐diameters and 6·1 m or 120 grain‐diameters were measured for two test particle sizes. Together with other available large scale field data, a dependence of the mean step length on particle diameter relative to the D₅₀ of the bed surface was found. During small floods the time used for movement represents only 2·7% of the total time from erosion to deposition. The increase in percentage of time being used for transport means that it then has to be regarded in stochastic transport models. Tracing the flow path of bed load particles between erosion and deposition sites is a step towards explaining the interactions between sediment transport and river morphology. Copyright © 2001 John Wiley & Sons, Ltd.     

A numerical study of flexural buckling of foliated rock slopes

The occurrence of foliated rock masses is common in mining environment. Methods employing continuum approximation in describing the deformation of such rock masses possess a clear advantage over methods where each rock layer and each inter‐layer interface (joint) is explicitly modelled. In devising such a continuum model it is imperative that moment (couple) stresses and internal rotations associated with the bending of the rock layers be properly incorporated in the model formulation. Such an approach will lead to a Cosserat‐type theory. In the present model, the behaviour of the intact rock layer is assumed to be linearly elastic and the joints are assumed to be elastic–perfectly plastic. Condition of slip at the interfaces are determined by a Mohr–Coulomb criterion with tension cut off at zero normal stress. The theory is valid for large deformations. The model is incorporated into the finite element program AFENA and validated against an analytical solution of elementary buckling problems of a layered medium under gravity loading. A design chart suitable for assessing the stability of slopes in foliated rock masses against flexural buckling failure has been developed. The design chart is easy to use and provides a quick estimate of critical loading factors for slopes in foliated rock masses. It is shown that the model based on Euler's buckling theory as proposed by Cavers (Rock Mechanics and Rock Engineering 1981; 14 :87–104) substantially overestimates the critical heights for a vertical slope and underestimates the same for sub‐vertical slopes. Copyright © 2001 John Wiley & Sons, Ltd.     

Evaluation of spatial variability in snow water equivalent for a high mountain catchment

Multivariate statistical analysis was used to explore relationships between catchment topography and spatial variability in snow accumulation and melt processes in a small headwater catchment in the Spanish Pyrenees. Manual surveys of snow depth and density provided information on the spatial distribution of snow water equivalent (SWE) and its depletion over the course of the 1997 and 1998 melt seasons. A number of indices expressing the topographic control on snow processes were extracted from a detailed digital elevation model of the catchment. Bivariate screening was used to assess the relative importance of these topographic indices in controlling snow accumulation at the start of the melt season, average melt rates and the timing of snow disappearance. This suggested that topographic controls on the redistribution of snow by wind are the most important influence on snow distribution at the start of the melt season. Furthermore, it appeared that spatial patterns of snow disappearance were largely determined by the distribution of snow water equivalent (SWE) at the start of the melt season, rather than by spatial variability in melt rates during the melt season. Binary regression tree models relating snow depth and disappearance date to terrain indices were then constructed. These explained 70–80% of the variance in the observed data. As well as providing insights into the influence of topography on snow processes, it is suggested that the techniques presented herein could be used in the parameterization of distributed snowmelt models, or in the design of efficient stratified snow surveys. Copyright © 2003 John Wiley & Sons, Ltd.