Estimation for partially observed Markov processes

Many stochastic process models for environmental data sets assume a process of relatively simple structure which is in some sense partially observed. That is, there is an underlying process (X_n, n 0) or (X_t, t 0) for which the parameters are of interest and physically meaningful, and an observable process (Y_n, n 0) or (Y_t, t 0) which depends on the X process but not otherwise on those parameters. Examples are wide ranging: the Y process may be the X process with missing observations; the Y process may be the X process observed with a noise component; the X process might constitute a random environment for the Y process, as with hidden Markov models; the Y process might be a lower dimensional function or reduction of the X process. In principle, maximum likelihood estimation for the X process parameters can be carried out by some form of the EM algorithm applied to the Y process data. In the paper we review some current methods for exact and approximate maximum likelihood estimation. We illustrate some of the issues by considering how to estimate the parameters of a stochastic Nash cascade model for runoff. In the case of k reservoirs, the outputs of these reservoirs form a k dimensional vector Markov process, of which only the kth coordinate process is observed, usually at a discrete sample of time points.     

冀西北长城纪宣龙式铁矿层中微体植物化石的发现及其意义

本文研究的是笔者等在冀西北长城系串岭沟组宣龙式铁矿层中发现的微体植物化石,这些化石都保存在铁质叠层石(肾状赤铁矿)和铁质核形石(鲕状赤铁矿)的基本层中。微化石以丝状体为主,部分为球状体。归属于原核生物蓝藻门颤藻科的两个属和色球藻科的一个属。化石层同位素年龄约在1800—1757Ma。这些化石与北美冈弗林特组微化石比较,既有些相似,又有些区别。该化石的发现为研究铁矿的成因,指示沉积环境及层位对比都很有意义。     

成都城市发展对热岛强度影响的主成份回归分析

本文对成都市总人口、建成区面积等11个因子、作了主成份回归L-S估计和M-估计,讨论了成都城市发展对“热岛”强度的主要影响因子。结果表明,城区房屋建筑面积及总人口数是影响城市气候(气温)的主要因子,其次为城市人口总户数、建成面积等。 文中,对回归方程进行了拟合计算,回归效果比较满意(尤其是稳健回归)。     

Comparison of structural and least-squares lines for estimating geologic relations

Two different goals in fitting straight lines to data are to estimate a true linear relation (physical law) and to predict values of the dependent variable with the smallest possible error. Regarding the first goal, a Monte Carlo study indicated that the structural-analysis (SA) method of fitting straight lines to data is superior to the ordinary least-squares (OLS) method for estimating true straight-line relations. Number of data points, slope and intercept of the true relation, and variances of the errors associated with the independent (X) and dependent (Y) variables influence the degree of agreement. For example, differences between the two line-fitting methods decrease as error in X becomes small relative to error in Y. Regarding the second goal—predicting the dependent variable—OLS is better than SA. Again, the difference diminishes as X takes on less error relative to Y. With respect to estimation of slope and intercept and prediction of Y, agreement between Monte Carlo results and large-sample theory was very good for sample sizes of 100, and fair to good for sample sizes of 20. The procedures and error measures are illustrated with two geologic examples.     

Visualization experiments of iron precipitates: Application for in-situ arsenic remediation

Laboratory experiments were carried out to acquire more insight and understanding of the phenomena associated with the in-situ arsenic remediation. Visualization techniques are the most informative for the detection of Fe(II) while flowing in soils. Green Rust (GR) was considered as representative of in-situ iron precipitates. In a visualization flat cell, the change in color of GR to orange, due to oxidation, was monitored by a digital camera and the images were analyzed giving the spatial and temporal distribution of Fe(II). Moreover, both oxygen and pH changes in time were recorded in two sections along the flow direction in the cell. The measured and calculated concentration profiles were compared and the actual reaction rates were predicted. The reaction rate constants measured in this study, under flowing conditions, are in a good agreement with the values obtained from batch experiments reported in the literature.     

Speciation of adsorbed arsenate on the surface of hydrous iron oxide

Adsorption of arsenate on hydrous iron oxide is an important process controlling geochemical cycling of arsenic in environment as well as the fate of arsenic-bearing mining wastes. The widely accepted view on the mechanism of adsorption is that arsenate is adsorbed via bidentate binuclear inner-sphere complexation. In this study, we characterized the arsenate-hydrous iron oxide sorption solids synthesized at pH=3-8 using Fourier transformed infrared spectroscopy （FTIR） and X-ray diffraction （XRD）. It has been determined that poorly crystalline ferric arsenate developed on the surface of iron oxide when arsenate was sorbed at acidic pH, while at alkaline pH the adsorption of arsenate was via bidentate complexation.     

XANES analysis of the mechanisms of arsenic removal in biological iron and manganese treatment unit

Biological iron and manganese removal utilizing indigenous iron and manganese oxidizing bacteria （IRB hereafter） in groundwater can also be applied to arsenic removal according to our pilot-scale test. The arsenic removal probably occurred through sorption and complexation of arsenic to iron and manganese oxides formed by enzymic action of IRB. We investigated the chemical properties of iron and manganese oxides in IRB floc and the valence state of arsenic sorbed to the floc to clarify the mechanisms of the arsenic [especially As （Ⅲ）] removal. The floc samples were collected from two drinking water plants using IRB （Jyoyo and Yamatokoriyama, Japan）, and our pilot - scale test site where arsenic and iron removal using IRB is under way （Mukoh, Japan）. The Jyoyo and Yamatokoriyama IRB floc samples were subjected to As （Ⅲ） and As（Ⅴ） sorption experiments. The elemental composition of the floc samples was measured. XANES spectra were collected on As, Fe and Mn K-edges at synchrotron radiation facility Spring 8 （Hyogo, Japan）. FT-IR and the X-ray diffraction spectra of the samples were also obtained. The IRB floc contained ca. 35 % Fe, 0.3%-3.5% Mn and 2%-6% P. The samples were highly amorphous and contained ferrihidrites and hydrated iron phosphate. According to XANES analyses of IRB, As associated with IRB was in ＋5 valence state when As （Ⅲ） （or As （Ⅴ）） was added in laboratory sorption test, Fe in ＋3 valence state, and Mn a mixture of＋3 and ＋4 valence states. Small shift was observed in the XANES spectra of IRB on As K-edge as the equilibration time of the sorption experiment was increased. Gradual oxidation of a small amount of As （Ⅲ） associated with IRB or change in arsenic binding with sorption site were the probable mechanism.     

Reservoir description using dynamic parameterisation selection with a combined stochastic and gradient search

There is a correspondence between flow in a reservoir and large scale permeability trends. This correspondence can be derived by constraining reservoir models using observed production data. One of the challenges in deriving the permeability distribution of a field using production data involves determination of the scale of resolution of the permeability. The Adaptive Multiscale Estimation (AME) seeks to overcome the problems related to choosing the resolution of the permeability field by a dynamic parameterisation selection. The standard AME uses a gradient algorithm in solving several optimisation problems with increasing permeability resolution. This paper presents a hybrid algorithm which combines a gradient search and a stochastic algorithm to improve the robustness of the dynamic parameterisation selection. At low dimension, we use the stochastic algorithm to generate several optimised models. We use information from all these produced models to find new optimal refinements, and start out new optimisations with several unequally suggested parameterisations. At higher dimensions we change to a gradient-type optimiser, where the initial solution is chosen from the ensemble of models suggested by the stochastic algorithm. The selection is based on a predefined criterion. We demonstrate the robustness of the hybrid algorithm on sample synthetic cases, which most of them were considered insolvable using the standard AME algorithm.     

Comparative Seismic Risk Studies for German Earthquake Regions on the Basis of the European Macroseismic Scale EMS-98

Within the framework of recent research projects, basic tools for GIS-based seismic risk assessment technologies were developed and applied to the building stock and regional particularities of German earthquake regions. Two study areas are investigated, being comparable by the level of seismic hazard and the hazard-consistent scenario events (related to mean return periods of 475, 2475 and 10000 years). Significant differences exist with respect to the number of inhabitants, the grade and extent of urbanisation, the quality and quantity of building inventory: the case study of Schmölln in Eastern Thuringia seems to be representative for the majority of smaller towns in Germany, the case study of Cologne (Köln) stands for larger cities. Due to the similarities of hazard and scenario intensities, the considerable differences do not only require proper decisions concerning the appropriate methods and acceptable efforts, they enable conclusions about future research strategies and needs for disaster reduction management. Not least important, results can sharpen the focus of public interest. Seismic risk maps are prepared for different scenario intensities recognising the scatter and uncertainties of site-dependent ground motion and also of the applied vulnerability functions. The paper illustrates the impact of model assumptions and the step-wise refinements of input variables like site conditions, building stock or vulnerability functions on the distribution of expected building damage within the study areas. Furthermore, and in contrast to common research strategies, results support the conclusion that in the case of stronger earthquakes the damage will be of higher concentration within smaller cities like Schmölln due to the site-amplification potential and/or the increased vulnerability of the building stock. The extent of damage will be pronounced by the large number of masonry buildings for which lower vulnerability classes have to be assigned. Due to the effect of deep sedimentary layers and the composition of building types, the urban centre of Cologne will be less affected by an earthquake of comparable intensity.     

T -distributed Random Fields: A Parametric Model for Heavy-tailedWell-log Data1

Histograms of observations from spatial phenomena are often found to be more heavy-tailed than Gaussian distributions, which makes the Gaussian random field model unsuited. A T-distributed random field model with heavy-tailed marginal probability density functions is defined. The model is a generalization of the familiar Student-T distribution, and it may be given a Bayesian interpretation. The increased variability appears cross-realizations, contrary to in-realizations, since all realizations are Gaussian-like with varying variance between realizations. The T-distributed random field model is analytically tractable and the conditional model is developed, which provides algorithms for conditional simulation and prediction, so-called T-kriging. The model compares favourably with most previously defined random field models. The Gaussian random field model appears as a special, limiting case of the T-distributed random field model. The model is particularly useful whenever multiple, sparsely sampled realizations of the random field are available, and is clearly favourable to the Gaussian model in this case. The properties of the T-distributed random field model is demonstrated on well log observations from the Gullfaks field in the North Sea. The predictions correspond to traditional kriging predictions, while the associated prediction variances are more representative, as they are layer specific and include uncertainty caused by using variance estimates.