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1.
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. 相似文献
2.
J. T. Shiau 《Stochastic Environmental Research and Risk Assessment (SERRA)》2003,17(1-2):42-57
Extreme hydrological events are inevitable and stochastic in nature. Characterized by multiple properties, the multivariate
distribution is a better approach to represent this complex phenomenon than the univariate frequency analysis. However, it
requires considerably more data and more sophisticated mathematical analysis. Therefore, a bivariate distribution is the most
common method for modeling these extreme events. The return periods for a bivariate distribution can be defined using either
separate single random variables or two joint random variables. In the latter case, the return periods can be defined using
one random variable equaling or exceeding a certain magnitude and/or another random variable equaling or exceeding another
magnitude or the conditional return periods of one random variable given another random variable equaling or exceeding a certain
magnitude. In this study, the bivariate extreme value distribution with the Gumbel marginal distributions is used to model
extreme flood events characterized by flood volume and flood peak. The proposed methodology is applied to the recorded daily
streamflow from Ichu of the Pachang River located in Southern Taiwan. The results show a good agreement between the theoretical
models and observed flood data.
The author wishes to thank the two anonymous reviewers for their constructive comments that improving the quality of this
work. 相似文献
3.
Properties and limitations of sequential indicator simulation 总被引：2，自引：0，他引：2
The sequential indicator algorithm is a widespread geostatistical simulation technique that relies on indicator (co)kriging and is applicable to a wide range of datasets. However, such algorithm comes up against several limitations that are often misunderstood. This work aims at highlighting these limitations, by examining what are the conditions for the realizations to reproduce the input parameters (indicator means and correlograms) and what happens with the other parameters (other two-point or multiple-point statistics). Several types of random functions are contemplated, namely: the mosaic model, random sets, models defined by multiple indicators and isofactorial models. In each case, the conditions for the sequential algorithm to honor the model parameters are sought after. Concurrently, the properties of the multivariate distributions are identified and some conceptual impediments are emphasized. In particular, the prior multiple-point statistics are shown to depend on external factors such as the total number of simulated nodes and the number and locations of the samples. As a consequence, common applications such as a flow simulation or a change of support on the realizations may lead to hazardous interpretations. 相似文献
4.
We consider a Bayesian model for inversion of observed amplitude variation with offset data into lithology/fluid classes, and study in particular how the choice of prior distribution for the lithology/fluid classes influences the inversion results. Two distinct prior distributions are considered, a simple manually specified Markov random field prior with a first-order neighbourhood and a Markov mesh model with a much larger neighbourhood estimated from a training image. They are chosen to model both horizontal connectivity and vertical thickness distribution of the lithology/fluid classes, and are compared on an offshore clastic oil reservoir in the North Sea. We combine both priors with the same linearized Gaussian likelihood function based on a convolved linearized Zoeppritz relation and estimate properties of the resulting two posterior distributions by simulating from these distributions with the Metropolis–Hastings algorithm. The influence of the prior on the marginal posterior probabilities for the lithology/fluid classes is clearly observable, but modest. The importance of the prior on the connectivity properties in the posterior realizations, however, is much stronger. The larger neighbourhood of the Markov mesh prior enables it to identify and model connectivity and curvature much better than what can be done by the first-order neighbourhood Markov random field prior. As a result, we conclude that the posterior realizations based on the Markov mesh prior appear with much higher lateral connectivity, which is geologically plausible. 相似文献
5.
Jun-Jih Liou Yuan-Fong Su Jie-Lun Chiang Ke-Sheng Cheng 《Stochastic Environmental Research and Risk Assessment (SERRA)》2011,25(2):235-251
In studies involving environmental risk assessment, Gaussian random field generators are often used to yield realizations
of a Gaussian random field, and then realizations of the non-Gaussian target random field are obtained by an inverse-normal
transformation. Such simulation process requires a set of observed data for estimation of the empirical cumulative distribution
function (ECDF) and covariance function of the random field under investigation. However, if realizations of a non-Gaussian
random field with specific probability density and covariance function are needed, such observed-data-based simulation process
will not work when no observed data are available. In this paper we present details of a gamma random field simulation approach
which does not require a set of observed data. A key element of the approach lies on the theoretical relationship between
the covariance functions of a gamma random field and its corresponding standard normal random field. Through a set of devised
simulation scenarios, the proposed technique is shown to be capable of generating realizations of the given gamma random fields. 相似文献
6.
S. Yue 《Stochastic Environmental Research and Risk Assessment (SERRA)》2001,15(3):244-260
The open literature reveals several types of bivariate exponential distributions. Of them only the Nagao–Kadoya distribution
(Nagao and Kadoya, 1970, 1971) has a general form with marginals that are standard exponential distributions and the correlation
coefficient being 0≤ρ<1. On the basis of the principle that if a theoretical probability distribution can represent statistical
properties of sample data, then the computed probabilities from the theoretical model should provide a good fit to observed
ones, numerical experiments are executed to investigate the applicability of the Nagao–Kadoya bivariate exponential distribution
for modeling the joint distribution of two correlated random variables with exponential marginals. Results indicate that this
model is suitable for analyzing the joint distribution of two exponentially distributed variables. The procedure for the use
of this model to represent the joint statistical properties of two correlated exponentially distributed variables is also
presented. 相似文献
7.
Gaussian conditional realizations are routinely used for risk assessment and planning in a variety of Earth sciences applications. Assuming a Gaussian random field, conditional realizations can be obtained by first creating unconditional realizations that are then post-conditioned by kriging. Many efficient algorithms are available for the first step, so the bottleneck resides in the second step. Instead of doing the conditional simulations with the desired covariance (F approach) or with a tapered covariance (T approach), we propose to use the taper covariance only in the conditioning step (half-taper or HT approach). This enables to speed up the computations and to reduce memory requirements for the conditioning step but also to keep the right short scale variations in the realizations. A criterion based on mean square error of the simulation is derived to help anticipate the similarity of HT to F. Moreover, an index is used to predict the sparsity of the kriging matrix for the conditioning step. Some guides for the choice of the taper function are discussed. The distributions of a series of 1D, 2D and 3D scalar response functions are compared for F, T and HT approaches. The distributions obtained indicate a much better similarity to F with HT than with T. 相似文献
8.
D. R. Helwade A. Subramanyam 《Stochastic Environmental Research and Risk Assessment (SERRA)》2010,24(2):271-281
In this paper, a certain bivariate exponential distribution is used for the spatial prediction. The unobserved random variable
is predicted by the projection onto the space of all linear combinations of the powers, up to degree m, of the observed random variables plus the constant 1. We obtain a solution by assuming that all the bivariate distributions
follow Gumbel’s type III or logistic form of bivariate exponential. The method is implemented on two data sets and the results
are presented. The predictions are compared with the original values through Mean Structural Similarity (MSSIM) index of Wang
et al. (IEEE Trans Image Process 13(4):600–612, 2004). Using the MSSIM index the proposed method is also compared with Ordinary Kriging and with Simple Kriging after normal score
transform. 相似文献
9.
Xinjun Tu Xiaohong Chen Mingwei Ma Qiang Zhang Yong Zhao 《Stochastic Environmental Research and Risk Assessment (SERRA)》2016,30(5):1317-1334
There are two kinds of uncertainty factors in modeling the bivariate distribution of hydrological droughts: the alteration of predefined critical ratios for pooling droughts and excluding minor droughts and the temporal variability of univariate and/or bivariate characteristics of droughts due to the impact of human activities. Daily flow data covering a period of 56 hydrological years from two gauging stations from a humid region in South China are used. The influences of alterations of threshold values of flow and critical ratios of pooling droughts and excluding minor droughts on drought properties are analyzed. Six conventional univariate models and three Archimedean copulas are employed to fit the marginal and joint distributions of drought properties, the Kolmogorov–Smirnov and Anderson–Darling methods are used for testing the goodness-of-fit of the univariate model, and the Cramer-von Mises method based on Rosenblatt’s transform is applied for the test of the bivariate model. The change point analysis of the copula parameter of bivariate distribution of droughts is first made. Results demonstrate that both the statistical characteristics of each drought property and their bivariate joint distributions are sensitive to the critical ratio of excluding minor droughts. A model can be selected to fit the marginal distribution for drought deficit volume or maximum deficit, but it is not determined for drought duration with the lower ratios of the pooling and excluding droughts. The statistical uncertainty of drought duration makes the modeling of bivariate joint distribution of drought duration and deficit volume or of drought duration and maximum deficit undermined. Change points significantly occurred in the period from the late 1970s to the middle 1980s for a single drought property and the copula parameter of their joint distribution due to the impact of human activities. The difference between two subseries separated by the change point is remarkable in the magnitudes of drought properties and the joint return periods. A copula function can be selected to optimally fit the bivariate distribution, provided that the critical ratios of pooling and excluding droughts are great enough such as the optimal value of 0.4 in the case study. It is valuable that the modeling and designing of the bivariate joint correlation and distribution of drought properties can be performed on the subseries separated by the change point of the copula parameter. 相似文献
10.
11.
Copula-based geostatistical modeling of continuous and discrete data including covariates 总被引：4，自引：3，他引：1
Hannes Kazianka Jürgen Pilz 《Stochastic Environmental Research and Risk Assessment (SERRA)》2010,24(5):661-673
It is common in geostatistics to use the variogram to describe the spatial dependence structure and to use kriging as the spatial prediction methodology. Both methods are sensitive to outlying observations and are strongly influenced by the marginal distribution of the underlying random field. Hence, they lead to unreliable results when applied to extreme value or multimodal data. As an alternative to traditional spatial modeling and interpolation we consider the use of copula functions. This paper extends existing copula-based geostatistical models. We show how location dependent covariates e.g. a spatial trend can be accounted for in spatial copula models. Furthermore, we introduce geostatistical copula-based models that are able to deal with random fields having discrete marginal distributions. We propose three different copula-based spatial interpolation methods. By exploiting the relationship between bivariate copulas and indicator covariances, we present indicator kriging and disjunctive kriging. As a second method we present simple kriging of the rank-transformed data. The third method is a plug-in prediction and generalizes the frequently applied trans-Gaussian kriging. Finally, we report on the results obtained for the so-called Helicopter data set which contains extreme radioactivity measurements. 相似文献
12.
13.
Stochastic weather generators are widely used in hydrological, environmental, and agricultural applications to simulate weather time series. However, such stochastic models produce random outputs hence the question on how representative the generated data are if obtained from only one simulation run (realization) as is common practice. In this study, the impact of different numbers of realizations (1, 25, 50, and 100) on the suitability of generated weather data was investigated. Specifically, 50 years of daily precipitation, and maximum and minimum temperatures were generated for three weather stations in the Western Lake Erie Basin (WLEB), using three widely used weather generators, CLIGEN, LARSWG and WeaGETS. Generated results were compared with 50 years of observed data. For all three generators, the analyses showed that one realization of data for 50 years of daily precipitation, and maximum and minimum temperatures may not be representative enough to capture essential statistical characteristics of the climate. Results from the three generators captured the essential statistical characteristics of the climate when the number of realizations was increased from 1 to 25, 50 or 100. Performance did not improve substantially when realizations were increased above 25. Results suggest the need for more than a single realization when generating weather data and subsequently utilizing in other models, to obtain suitable representations of climate. 相似文献
14.
Xavier Emery 《Stochastic Environmental Research and Risk Assessment (SERRA)》2010,24(2):211-219
The multi-Gaussian model is used in geostatistical applications to predict functions of a regionalized variable and to assess
uncertainty by determining local (conditional to neighboring data) distributions. The model relies on the assumption that
the regionalized variable can be represented by a transform of a Gaussian random field with a known mean value, which is often
a strong requirement. This article presents two variations of the model to account for an uncertain mean value. In the first
one, the mean of the Gaussian random field is regarded as an unknown non-random parameter. In the second model, the mean of
the Gaussian field is regarded as a random variable with a very large prior variance. The properties of the proposed models
are compared in the context of non-linear spatial prediction and uncertainty assessment problems. Algorithms for the conditional
simulation of Gaussian random fields with an uncertain mean are also examined, and problems associated with the selection
of data in a moving neighborhood are discussed. 相似文献
15.
The purpose of this article is to show how Bayesian belief networks can beused in analysis of the sequence of the earthquakes which have occurred in a region, to study the interaction among the variables characterizing eachevent. These relationships can be represented by means of graphs consistingof vertices and edges; the vertices correspond to random variables, whilethe edges express properties of conditional independence. We have examinedItalian seismicity as reported in two data bases, the NT4.1.1 catalogue and the ZS.4 zonation, and taken into account three variables: the size of thequake, the time elapsed since the previous event, and the time before the subsequent one. Assigning different independence relationships among these variables, first two couples of bivariate models, and then eight trivariatemodels have been defined. After presenting the main elements constituting a Bayesian belief network, we introduce the principal methodological aspects concerning estimation and model comparison. Following a fully Bayesian approach, prior distributions are assigned on both parameters and structuresby combining domain knowledge and available information on homogeneous seismogenic zones. Two case studies are used to illustrate in detail the procedure followed to evaluate the fitting of each model to the data sets andcompare the performance of alternative models. All eighty Italian seismogenic zones have been analysed in the same way; the results obtained are reportedbriefly. We also show how to account for model uncertainty in predicting a quantity of interest, such as the time of the next event. 相似文献
16.
B. G. Hankin K. J. Beven 《Stochastic Environmental Research and Risk Assessment (SERRA)》1998,12(6):377-396
In a special opportunity, detailed measurements of the flow in an overbank flow in the Flood Channel Facility at HR Wallingford
were used in conjunction with tracer test data to assess the effectiveness of dispersion models based around random particle
tracking (RPT). Ten different RPT models based on different assumptions and levels of information about the nature of the
Lagrangian velocity field were investigated. Multiple simulations were used to calibrate variable parameters controlling the
average magnitude of the perturbations for each model by comparison with observed concentrations at one cross-section. The
calibrated models were then used to predict concentration distributions further downstream. Several of the calibrated models
showed close agreement between observed and predicted concentration distributions. The most complex models using the most
information about the velocity distributions were no better (and in some cases worse) in prediction than the simplest models
investigated. It would appear that our knowledge of the system, despite the quality of the experiments, is too uncertain to
infer a precise model structure. 相似文献
17.
In a special opportunity, detailed measurements of the flow in an overbank flow in the Flood Channel Facility at HR Wallingford
were used in conjunction with tracer test data to assess the effectiveness of dispersion models based around random particle
tracking (RPT). Ten different RPT models based on different assumptions and levels of information about the nature of the
Lagrangian velocity field were investigated. Multiple simulations were used to calibrate variable parameters controlling the
average magnitude of the perturbations for each model by comparison with observed concentrations at one cross-section. The
calibrated models were then used to predict concentration distributions further downstream. Several of the calibrated models
showed close agreement between observed and predicted concentration distributions. The most complex models using the most
information about the velocity distributions were no better (and in some cases worse) in prediction than the simplest models
investigated. It would appear that our knowledge of the system, despite the quality of the experiments, is too uncertain to
infer a precise model structure. 相似文献
18.
A new bivariate Gamma distribution generated from functional scale parameter with application to drought data 总被引：1，自引：0，他引：1
Muhammad Mohsin Albrecht Gebhardt Jürgen Pilz Gunter Spöck 《Stochastic Environmental Research and Risk Assessment (SERRA)》2013,27(5):1039-1054
Univariate and bivariate Gamma distributions are among the most widely used distributions in hydrological statistical modeling and applications. This article presents the construction of a new bivariate Gamma distribution which is generated from the functional scale parameter. The utilization of the proposed bivariate Gamma distribution for drought modeling is described by deriving the exact distribution of the inter-arrival time and the proportion of drought along with their moments, assuming that both the lengths of drought duration (X) and non-drought duration (Y) follow this bivariate Gamma distribution. The model parameters of this distribution are estimated by maximum likelihood method and an objective Bayesian analysis using Jeffreys prior and Markov Chain Monte Carlo method. These methods are applied to a real drought dataset from the State of Colorado, USA. 相似文献
19.
Chuanrong Zhang Weidong Li 《Stochastic Environmental Research and Risk Assessment (SERRA)》2008,22(2):217-230
Simulating fields of categorical geospatial variables from samples is crucial for many purposes, such as spatial uncertainty
assessment of natural resources distributions. However, effectively simulating complex categorical variables (i.e., multinomial
classes) is difficult because of their nonlinearity and complex interclass relationships. The existing pure Markov chain approach
for simulating multinomial classes has an apparent deficiency—underestimation of small classes, which largely impacts the
usefulness of the approach. The Markov chain random field (MCRF) theory recently proposed supports theoretically sound multi-dimensional
Markov chain models. This paper conducts a comparative study between a MCRF model and the previous Markov chain model for
simulating multinomial classes to demonstrate that the MCRF model effectively solves the small-class underestimation problem.
Simulated results show that the MCRF model fairly produces all classes, generates simulated patterns imitative of the original,
and effectively reproduces input transiograms in realizations. Occurrence probability maps are estimated to visualize the
spatial uncertainty associated with each class and the optimal prediction map. It is concluded that the MCRF model provides
a practically efficient estimator for simulating multinomial classes from grid samples. 相似文献
20.
Droughts are one of the normal and recurrent climatic phenomena on Earth. However, recurring prolonged droughts have caused far‐reaching and diverse impacts because of water deficits. This study aims to investigate the hydrological droughts of the Yellow River in northern China. Since drought duration and drought severity exhibit significant correlation, a bivariate distribution is used to model the drought duration and severity jointly. However, drought duration and drought severity are often modelled by different distributions; the commonly used bivariate distributions cannot be applied. In this study, a copula is employed to construct the bivariate drought distribution. The copula is a function that links the univariate marginal distributions to form the bivariate distribution. The bivariate return periods are also established to explore the drought characteristics of the historically noticeable droughts. The results show that the return period of the drought that occurred in late 1920s to early 1930s is 105 years. The significant 1997 dry‐up phenomenon that occurred in the downstream Yellow River (resulting from the 1997–1998 drought) only has a return period of 4·4 years and is probably induced by two successive droughts and deteriorated by other factors, such as human activities. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献