A Blocking Markov Chain Monte Carlo Method for Inverse Stochastic Hydrogeological Modeling

An adequate representation of the detailed spatial variation of subsurface parameters for underground flow and mass transport simulation entails heterogeneous models. Uncertainty characterization generally calls for a Monte Carlo analysis of many equally likely realizations that honor both direct information (e.g., conductivity data) and information about the state of the system (e.g., piezometric head or concentration data). Thus, the problems faced is how to generate multiple realizations conditioned to parameter data, and inverse-conditioned to dependent state data. We propose using Markov chain Monte Carlo approach (MCMC) with block updating and combined with upscaling to achieve this purpose. Our proposal presents an alternative block updating scheme that permits the application of MCMC to inverse stochastic simulation of heterogeneous fields and incorporates upscaling in a multi-grid approach to speed up the generation of the realizations. The main advantage of MCMC, compared to other methods capable of generating inverse-conditioned realizations (such as the self-calibrating or the pilot point methods), is that it does not require the solution of a complex optimization inverse problem, although it requires the solution of the direct problem many times.     

Comparative analysis of different techniques for spatial interpolation of rainfall data to create a serially complete monthly time series of precipitation for Sicily,Italy

The availability of good and reliable rainfall data is fundamental for most hydrological analyses and for the design and management of water resources systems. However, in practice, precipitation records often suffer from missing data values mainly due to malfunctioning of raingauge for specific time periods. This is an important issue in practical hydrology because it affects the continuity of rainfall data and ultimately influences the results of hydrologic studies which use rainfall as input. Many methods to estimate missing rainfall data have been proposed in literature and, among these, most are based on spatial interpolation algorithms.     

On the physical geometry concept at the basis of space/time geostatistical hydrology

The objective of this paper is to show that the structure of the spatiotemporal continuum has important implications in practical stochastic hydrology (e.g., geostatistical analysis of hydrologic sites) and is not merely an abstract mathematical concept. We propose that the concept of physical geometry as a spatiotemporal continuum with properties that are empirically defined is important in hydrologic analyses, and that the elements of the spatiotemporal geometry (e.g., coordinate system and space/time metric) should be selected based on the physical properties of the hydrologic processes. We investigate the concept of space/time distance (metric) in various physical spaces, and its implications for hydrologic modeling. More specifically, we demonstrate that physical geometry plays a crucial role in the determination of appropriate spatiotemporal covariance models, and it can affect the results of geostatistical operations involved in spatiotemporal hydrologic mapping.     

Intrinsic random function of order<Emphasis Type="Italic"> k</Emphasis> kriging of electrical resistivity data for estimating the extent of saltwater intrusion in a coastal aquifer system

A saltwater intrusion study using electrical resistivity distribution was conducted in a coastal aquifer system in the southeastern part of Busan, Korea. This aquifer system is divided into four layers according to the hydrogeologic characteristics, and the horizontal extent of intruded saltwater is determined at each layer through the geostatistical interpretation of electrical resistivity data. Intrinsic random function of order k (IRF-k) kriging is performed with covariance models to produce the plane of spatial mean resistivities. The kriged estimates are evaluated by cross validation, and they showed a good agreement with the true values. The statistics of cross validation represented low errors for the estimates. In the resistivity contour maps more than 5 m below the surface, a dominant direction of saltwater intrusion was observed beginning from the east side. These results led the authors to conclude that the application of geostatistical technique to electrical resistivity data is useful for assessing saltwater intrusion in a coastal aquifer system.     

A simple model for spatial rainfall fields

Spatial rainfall amounts accumulated over short to medium periods of time, say a few days, tend to have a probabilistic structure with very distinctive features. Some of these that are specially relevant for the purpose of spatial modeling are the presence of mixed sampling distributions, right skewed distributions conditional on rainfall occurrence, and a complex spatial association structure. The goal of this work is to construct a family for the bivariate distributions of spatial rainfall fields that incorporates these distinctive features. It is based on the separate modeling of spatial occurrence of rainfall and the spatial distribution of positive rainfalls. The main properties of the bivariate distributions are derived, and some properties of the random field realizations are illustrated through simulation. Some limitations of the proposed model are also discussed.     

Spatial variability and temporal stability of throughfall water under a dominant beech (Fagus sylvatica L.) tree in relationship to canopy cover

Although the spatial heterogeneity of throughfall water (TF) under forest canopies has been related to vegetation structure in several forest types, few reports have been made of the driving factors of small-scale TF variability in deciduous stands. Therefore, the spatial variability of the amount of TF water under one dominant beech (Fagus sylvatica L.) tree was quantified in high temporal and spatial resolution over a 2-year period to examine the temporal stability of spatial TF variability and to relate spatial TF patterns to canopy cover determined photographically above each TF collector (n = 48). The spatial variability of TF was significantly higher during the leafed periods (coefficient of variation (CV) = 18%) than during the leafless periods (CV = 8%), and a strong negative relationship was observed between the CV of event TF and the TF fraction of rainfall in the open field. Geostatistical analysis showed that the cumulative TF water during the leafed periods was spatially correlated up to a distance of 3–4 m. There was a significant temporal stability of spatial TF patterns in the growing periods and in the dormant periods, but patterns differed largely between the two periods of the year. TF water during the growing periods significantly decreased with increasing canopy cover above the sampling locations (r = −0.54, p = 0.014, n = 20), but was more closely correlated with branch cover (r = −0.77, p < 0.001). However, the spatial pattern of TF during defoliated conditions was not related to the measured variation in branch cover.     

Combining categorical and continuous spatial information within the Bayesian maximum entropy paradigm

Due to the fast pace increasing availability and diversity of information sources in environmental sciences, there is a real need of sound statistical mapping techniques for using them jointly inside a unique theoretical framework. As these information sources may vary both with respect to their nature (continuous vs. categorical or qualitative), their spatial density as well as their intrinsic quality (soft vs. hard data), the design of such techniques is a challenging issue. In this paper, an efficient method for combining spatially non-exhaustive categorical and continuous data in a mapping context is proposed, based on the Bayesian maximum entropy paradigm. This approach relies first on the definition of a mixed random field, that can account for a stochastic link between categorical and continuous random fields through the use of a cross-covariance function. When incorporating general knowledge about the first- and second-order moments of these fields, it is shown that, under mild hypotheses, their joint distribution can be expressed as a mixture of conditional Gaussian prior distributions, with parameters estimation that can be obtained from entropy maximization. A posterior distribution that incorporates the various (soft or hard) continuous and categorical data at hand can then be obtained by a straightforward conditionalization step. The use and potential of the method is illustrated by the way of a simulated case study. A comparison with few common geostatistical methods in some limit cases also emphasizes their similarities and differences, both from the theoretical and practical viewpoints. As expected, adding categorical information may significantly improve the spatial prediction of a continuous variable, making this approach powerful and very promising.     

Seabird guano influences on desert islands: soil chemistry and herbaceous species richness and productivity

An understanding of the effects of guano deposition on arid soil chemistry and the consequences for plant communities is lacking. This study examined patterns of herbaceous species richness and productivity, soil chemistry, soil moisture and soil respiration on 11 islands in the Gulf of California, six of which receive seabird guano deposition. Species richness was significantly lower on islands with guano (“Bird” islands) than islands without guano (“Non-bird” islands), with very little overlap in species composition; however, productivity was significantly greater on Bird than on Non-bird islands. As expected, Bird island soils had higher concentrations of NO₃⁻, NH₄⁺ and total nitrogen (N) than Non-bird island soils; and, measurements of δ¹⁵N indicate that the higher concentrations of N were derived from guano. We also found that soil moisture and respiration were significantly higher, but pH was significantly lower, on Bird than Non-bird islands. These results suggest that guano deposition in deserts stimulates productivity—even in dry years—due to elevated N and, indirectly, soil moisture. Guano deposition also results in a decrease in species richness and a change in species composition probably due to elevated N, N toxicity, or low pH. However, we also found that pH varied more on Bird than on Non-bird islands; and that salinity—while not different between island types—was significantly patchier on Bird than on Non-Bird islands. These results suggest that guano deposition affects not only the general chemical composition of soils, but also results in greater spatial variation in soil chemical composition, which may ultimately affect species richness and composition. Therefore, understanding spatial patterning in soil chemistry as a result of guano deposition is critical for understanding guano effects on plant richness and productivity.     

Three-dimensional liquefaction potential analysis using geostatistical interpolation

We applied three-dimensional geostatistical interpolation to evaluate the extent of liquefiable materials at two sites that liquefied during the 1994 Northridge Earthquake. The sites were the Balboa Blvd site and the Wynne Ave. site located in the alluvial San Fernando Valley. The estimated peak ground accelerations at the sites are 0.84 g (Balboa Blvd) and 0.51 g (Wynne Ave.). These sites were chosen because surface effects due to liquefaction were not predicted using available techniques based on thickness and depth of liquefiable layers (Ishihara [Ishihara K. Stability of natural deposits during earthquakes. Proceedings of the 11th international conference on soil mechanics and foundation engineering, vol. 1. Rotterdam, The Netherlands: A.A. Balkema; 1985. p. 321–76.]) and the Liquefaction Potential Index (Iwasaki et al. [Iwasaki T, Tatsuoka F, Tokida K, Yasuda S. A practical method for assessing soil liquefaction potential based on case studies at various sites in Japan. In: Proceedings of the second international conference on microzonation, San Francisco; 1978. p. 885–96.]). During the earthquake, both sites experienced surface effects including ground cracking and extension as a result of liquefaction. Foundations and buried utilities were damaged at both sites. The sites were investigated after the event by researchers with the United States Geologic Survey using standard penetration tests (SPT) and cone penetration tests. In this paper, liquefaction potential was estimated for each soil sample using results from SPTs according to the updated Seed and Idriss simplified procedure. The probability of liquefaction was estimated by applying an indicator transform to the results of the liquefaction potential calculation. We compared our results to detailed geologic mapping of the sites performed by other researchers. Using geostatistical interpolation to estimate the probability of liquefaction is a useful supplement to geologic evaluation of liquefaction potential. The geostatistical analysis provides an estimate of the continuous volume of liquefiable soil along with an assessment of confidence in an interpolation. The probability of liquefaction volumes compare well with those predicted using geologic interpretations.     

地质统计学在固体矿产资源／储量分类中的应用

讨论了地质统计学（空间信息统计学）在固体矿产资源／储量分类中的若干问题，主要包括：1）矿产资源／储量估计方法的选择；2）两个重要概念－估计方差及离差方差；3）支持效应及其在矿产资源／储量评估中的重要作用；4）特异值（特高品位）的识别及处理方法；5）关于吨位－品位曲线；6）确定最优勘探网度及取样间距（及位置）的地质统计学方法；7）地质统计学在确定最优矿床工业指标中的应用；8）储量计算及固体矿产资源／储量分类的地质统计学实施方案。