共查询到20条相似文献，搜索用时 390 毫秒
1.
A bivariate meta-Gaussian density for use in hydrology 总被引：3，自引：0，他引：3
Convenient bivariate densities found in the literature are often unsuitable for modeling hydrologic variates. They either
constrain the range of association between variates, or fix the form of the marginal distributions. The bivariate meta-Gaussian
density is constructed by embedding the normal quantile transform of each variate into the Gaussian law. The density can represent
a full range of association between variates and admits arbitrarily specified marginal distributions. Modeling and estimation
can be decomposed into i) independent analyses of the marginal distributions, and ii) investigation of the dependence structure.
Both statistical and judgmental estimation procedures are possible. Some comparisons to recent applications of bivariate densities
in the hydrologic literature motivate and illustrate the model. 相似文献
2.
Certain bivariate densities constructed from marginals have recently been suggested as models of hydrologic variates such as rainfall intensity and depth. It is pointed out that (i) these densities belong to the families of the Farlie-Gumbel-Morgenstern densities and the Farlie polynomial densities, which have been extensively studied in the statistical literature, and that (ii) these densities have a limited potential applicability in hydrology since they can model only weakly associated variates, whose product-moment correlationR is within the range |R|1/3, under the first family of densities, and |R|1/2 under the second family. 相似文献
3.
D. Long R. Krzysztofowicz 《Stochastic Environmental Research and Risk Assessment (SERRA)》1992,6(1):47-54
Certain bivariate densities constructed from marginals have recently been suggested as models of hydrologic variates such as rainfall intensity and depth. It is pointed out that (i) these densities belong to the families of the Farlie-Gumbel-Morgenstern densities and the Farlie polynomial densities, which have been extensively studied in the statistical literature, and that (ii) these densities have a limited potential applicability in hydrology since they can model only weakly associated variates, whose product-moment correlationR is within the range |R|1/3, under the first family of densities, and |R|1/2 under the second family. 相似文献
4.
T. I. Harrold A. Sharma S. Sheather 《Stochastic Environmental Research and Risk Assessment (SERRA)》2001,15(4):310-324
Mutual information is a generalised measure of dependence between any two variables. It can be used to quantify non-linear
as well as linear dependence between any two variables. This makes mutual information an attractive alternative to the use
of the correlation coefficient, which can only quantify the linear dependence pattern. Mutual information is especially suited
for application to hydrological problems, because the dependence between any two hydrologic variables is seldom linear in
nature. Calculation of the mutual information score involves estimation of the marginal and joint probability density functions
of the two variables. This paper uses nonparametric kernel density estimation methods to estimate the probability density
functions. Accurate estimation of the mutual information score using kernel methods requires selection of appropriate smoothing
parameters (bandwidths) for use with the kernels. The aim of this paper is to obtain a practical method for bandwidth selection
for calculation of the mutual information score. In this paper, the lag-one dependence structures of several autocorrelated
time series are analysed using mutual information (note that this produces the lag-one auto-MI score, the analog of the lag-one
autocorrelation). Empirical trials are used to select appropriate bandwidths for a range of underlying autoregressive and
autoregressive-moving average models with normal or near-normal parent distributions. Expressions for reasonable bandwidth
choices under these conditions are proposed. 相似文献
5.
A new approach for streamflow simulation using nonparametric methods was described in a recent publication (Sharma et al.
1997). Use of nonparametric methods has the advantage that they avoid the issue of selecting a probability distribution and
can represent nonlinear features, such as asymmetry and bimodality that hitherto were difficult to represent, in the probability
structure of hydrologic variables such as streamflow and precipitation. The nonparametric method used was kernel density estimation,
which requires the selection of bandwidth (smoothing) parameters. This study documents some of the tests that were conduced
to evaluate the performance of bandwidth estimation methods for kernel density estimation. Issues related to selection of
optimal smoothing parameters for kernel density estimation with small samples (200 or fewer data points) are examined. Both
reference to a Gaussian density and data based specifications are applied to estimate bandwidths for samples from bivariate
normal mixture densities. The three data based methods studied are Maximum Likelihood Cross Validation (MLCV), Least Square
Cross Validation (LSCV) and Biased Cross Validation (BCV2). Modifications for estimating optimal local bandwidths using MLCV
and LSCV are also examined. We found that the use of local bandwidths does not necessarily improve the density estimate with
small samples. Of the global bandwidth estimators compared, we found that MLCV and LSCV are better because they show lower
variability and higher accuracy while Biased Cross Validation suffers from multiple optimal bandwidths for samples from strongly
bimodal densities. These results, of particular interest in stochastic hydrology where small samples are common, may have
importance in other applications of nonparametric density estimation methods with similar sample sizes and distribution shapes.
Received: November 12, 1997 相似文献
6.
A. Sharma U. Lall D. G. Tarboton 《Stochastic Environmental Research and Risk Assessment (SERRA)》1998,12(1):33-52
A new approach for streamflow simulation using nonparametric methods was described in a recent publication (Sharma et al.
1997). Use of nonparametric methods has the advantage that they avoid the issue of selecting a probability distribution and
can represent nonlinear features, such as asymmetry and bimodality that hitherto were difficult to represent, in the probability
structure of hydrologic variables such as streamflow and precipitation. The nonparametric method used was kernel density estimation,
which requires the selection of bandwidth (smoothing) parameters. This study documents some of the tests that were conduced
to evaluate the performance of bandwidth estimation methods for kernel density estimation. Issues related to selection of
optimal smoothing parameters for kernel density estimation with small samples (200 or fewer data points) are examined. Both
reference to a Gaussian density and data based specifications are applied to estimate bandwidths for samples from bivariate
normal mixture densities. The three data based methods studied are Maximum Likelihood Cross Validation (MLCV), Least Square
Cross Validation (LSCV) and Biased Cross Validation (BCV2). Modifications for estimating optimal local bandwidths using MLCV
and LSCV are also examined. We found that the use of local bandwidths does not necessarily improve the density estimate with
small samples. Of the global bandwidth estimators compared, we found that MLCV and LSCV are better because they show lower
variability and higher accuracy while Biased Cross Validation suffers from multiple optimal bandwidths for samples from strongly
bimodal densities. These results, of particular interest in stochastic hydrology where small samples are common, may have
importance in other applications of nonparametric density estimation methods with similar sample sizes and distribution shapes.
Received: November 12, 1997 相似文献
7.
利用西江下游马口水文站1959 2009年月径流量数据计算径流干旱指数,经游程理论提取了水文干旱特征值.应用Copula函数分析水文干旱强度和历时之间的联合概率分布.对构建的干旱历时和强度联合分布模式进行分析,结果表明:(1)径流干旱历时和强度之间具有高关联性,秩相关系数达0.617;(2)三参数Weibull分布较好地描述了干旱历时和强度的边缘分布特征;(3)经拟合优度检验结果优选的干旱历时和强度之间的较优连接函数为Archimedean类的Gumbel-Hougaard Copula函数;(4)5～10年重现期和20年重现期的水文干旱分别达到了重旱级别和特旱级别;(5)干旱历时和强度之间的遭遇概率可为特定干旱历时与水文干旱级别或特定干旱强度与干旱历时之间的对应关系提供概率意义上的干旱特征诊断与预测. 相似文献
8.
Use of a nonstationary copula to predict future bivariate low flow frequency in the Connecticut river basin 总被引：1，自引：0，他引：1 
下载免费PDF全文
下载免费PDF全文 Frequency analysis of streamflow provides an essential ingredient in our understanding of hydrologic events and provides needed guidance in the design and management of water resources infrastructure. However, traditional hydrologic approaches often fail to include important external effects that can result in unpredictable or unforeseen changes in streamflow. Moreover, previous studies investigating multiple characteristics of streamflow do not address a nonstationary approach. This study explores nonstationary frequency analysis of bivariate characteristics, including occurrence and severity, of annual low flow in the Connecticut River Basin, United States. To investigate bivariate low flow frequency, copulas and their marginal distributions are constructed by using stationary and nonstationary approaches. Our study results indicate that streamflow used in this study demonstrate significant nonstationarity. Over time, the occurrence and severity of low flows are shown to be lower with the same probability based on the results of nonstationary copulas. Bivariate low flow frequencies in the years 1970, 2000, and 2030, and their joint return periods are estimated under the nonstationary copulas. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
9.
There are two basic approaches for estimating flood quantiles: a parametric and a nonparametric method. In this study, the comparisons of parametric and nonparametric models for annual maximum flood data of Goan gauging station in Korea were performed based on Monte Carlo simulation. In order to consider uncertainties that can arise from model and data errors, kernel density estimation for fitting the sampling distributions was chosen to determine safety factors (SFs) that depend on the probability model used to fit the real data. The relative biases of Sheater and Jones plug-in (SJ) are the smallest in most cases among seven bandwidth selectors applied. The relative root mean square errors (RRMSEs) of the Gumbel (GUM) are smaller than those of any other models regardless of parent models considered. When the Weibull-2 is assumed as a parent model, the RRMSEs of kernel density estimation are relatively small, while those of kernel density estimation are much bigger than those of parametric methods for other parent models. However, the RRMSEs of kernel density estimation within interpolation range are much smaller than those for extrapolation range in comparison with those of parametric methods. Among the applied distributions, the GUM model has the smallest SFs for all parent models, and the general extreme value model has the largest values for all parent models considered. 相似文献
10.
Monitoring sediment yields from catchments is important for assessing overall denudation rates and the impact of environmental change. One of the methods used to assess sediment yield is by quantifying sedimentation rates in reservoirs, lakes or small ponds. Before reliable sediment yield values (t ha?1 a?1) can be computed from such sedimentation records, the measured sediment volumes need to be converted to sediment masses using representative values of the dry sediment bulk density. In textbooks, simple relations predicting dry sediment bulk density from sediment texture, time since deposition and hydrologic condition are presented. In this study, 13 small flood retention ponds in central Belgium were sampled to reveal the variability in dry sediment bulk density and to test the commonly used relations to predict dry sediment bulk density. Dry sediment bulk density varies not only between the selected ponds (0·78–1·35 t m?3) but also within individual ponds (coefficient of variation at 95 per cent ranges from 7 to 80 per cent). The observed variability can be attributed primarily to the hydrologic condition of the retention pond and, also, to sediment texture. The existing relations are not a reliable predictor for the observed dry bulk densities, because they are primarily based on sediment texture. Thus, when using volumetric sedimentation data from small ponds with varying hydrologic condition to predict sediment yield, existing relations predicting dry sediment bulk density cannot be applied. Instead, frequent and dense sampling of sediments is necessary to calculate a representative value of the dry sediment bulk density. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
11.
Kasemsan Manomaiphiboon Sun-Kyoung Park Armistead G. Russell 《Stochastic Environmental Research and Risk Assessment (SERRA)》2008,22(2):159-168
Probabilistic characterization of environmental variables or data typically involves distributional fitting. Correlations,
when present in variables or data, can considerably complicate the fitting process. In this work, effects of high-order correlations
on distributional fitting were examined, and how they are technically accounted for was described using two multi-dimensional
formulation methods: maximum entropy (ME) and Koehler–Symanowski (KS). The ME method formulates a least-biased distribution
by maximizing its entropy, and the KS method uses a formulation that conserves specified marginal distributions. Two bivariate
environmental data sets, ambient particulate matter and water quality, were chosen for illustration and discussion. Three
metrics (log-likelihood function, root-mean-square error, and bivariate Kolmogorov–Smirnov statistic) were used to evaluate
distributional fit. Bootstrap confidence intervals were also employed to help inspect the degree of agreement between distributional
and sample moments. It is shown that both methods are capable of fitting the data well and have the potential for practical
use. The KS distributions were found to be of good quality, and using the maximum likelihood method for the parameter estimation
of a KS distribution is computationally efficient. 相似文献
12.
依据在中国西藏高原地区得到的6幅云闪放电通道的光谱,由谱线波长、相对强度和跃迁几率等信息,结合等离子体理论,计算了云闪放电通道的温度和电子密度;进而,利用Saha方程、电荷守恒和粒子数守恒方程,得到了粒子处于各电离级上的数密度、通道质量密度、压强和平均电离度等参数,并对云闪通道内部粒子数分布特点进行了分析.结果表明,与地闪回击通道类似,云闪通道接近于完全电离,通道内部以单次电离的离子为主,且NII离子数密度最高.具有较高温度的通道位置处,中性和一次以上电离离子数密度的绝对值和相对值都较高,但是,不同温度下NII、OII、ArII粒子的相对浓度变化不大.与地闪回击通道不同,云闪同一放电通道内不同位置处粒子数密度差异较大,且沿通道没有显示规律性变化,通道压强从零点几到几兆帕. 相似文献
13.
This study uses elliptical copulas and transition probabilities for uncertainty modeling of categorical spatial data. It begins by discussing the expressions of the cumulative distribution function and probability density function of two major elliptical copulas: Gaussian copula and t copula. The basic form of spatial copula discriminant function is then derived based on Bayes’ theorem, which consists of three parts: the prior probability, the conditional marginal densities, and the conditional copula density. Finally, three kinds of parameter estimation methods are discussed, including maximum likelihood estimation, inference functions for margins and canonical maximum likelihood (CML). To avoid making assumptions on the form of marginal distributions, the CML approach is adopted in the real-world case study. Results show that the occurrence probability maps generated by these two elliptical copulas are similar to each other. However, the prediction map interpolated by Gaussian copula has a relatively higher classification accuracy than t copula. 相似文献
14.
Equifinality of formal (DREAM) and informal (GLUE) Bayesian approaches in hydrologic modeling? 总被引：1，自引：0，他引：1
Jasper A. Vrugt Cajo J. F. ter Braak Hoshin V. Gupta Bruce A. Robinson 《Stochastic Environmental Research and Risk Assessment (SERRA)》2009,23(7):1011-1026
In recent years, a strong debate has emerged in the hydrologic literature regarding what constitutes an appropriate framework for uncertainty estimation. Particularly, there is strong disagreement whether an uncertainty framework should have its roots within a proper statistical (Bayesian) context, or whether such a framework should be based on a different philosophy and implement informal measures and weaker inference to summarize parameter and predictive distributions. In this paper, we compare a formal Bayesian approach using Markov Chain Monte Carlo (MCMC) with generalized likelihood uncertainty estimation (GLUE) for assessing uncertainty in conceptual watershed modeling. Our formal Bayesian approach is implemented using the recently developed differential evolution adaptive metropolis (DREAM) MCMC scheme with a likelihood function that explicitly considers model structural, input and parameter uncertainty. Our results demonstrate that DREAM and GLUE can generate very similar estimates of total streamflow uncertainty. This suggests that formal and informal Bayesian approaches have more common ground than the hydrologic literature and ongoing debate might suggest. The main advantage of formal approaches is, however, that they attempt to disentangle the effect of forcing, parameter and model structural error on total predictive uncertainty. This is key to improving hydrologic theory and to better understand and predict the flow of water through catchments. 相似文献
15.
Jasper A. Vrugt Cajo J. F. ter Braak Hoshin V. Gupta Bruce A. Robinson 《Stochastic Environmental Research and Risk Assessment (SERRA)》2009,23(7):1061-1062
In recent years, a strong debate has emerged in the hydrologic literature regarding what constitutes an appropriate framework
for uncertainty estimation. Particularly, there is strong disagreement whether an uncertainty framework should have its roots
within a proper statistical (Bayesian) context, or whether such a framework should be based on a different philosophy and
implement informal measures and weaker inference to summarize parameter and predictive distributions. In this paper, we compare
a formal Bayesian approach using Markov Chain Monte Carlo (MCMC) with generalized likelihood uncertainty estimation (GLUE)
for assessing uncertainty in conceptual watershed modeling. Our formal Bayesian approach is implemented using the recently
developed differential evolution adaptive metropolis (DREAM) MCMC scheme with a likelihood function that explicitly considers
model structural, input and parameter uncertainty. Our results demonstrate that DREAM and GLUE can generate very similar estimates
of total streamflow uncertainty. This suggests that formal and informal Bayesian approaches have more common ground than the
hydrologic literature and ongoing debate might suggest. The main advantage of formal approaches is, however, that they attempt
to disentangle the effect of forcing, parameter and model structural error on total predictive uncertainty. This is key to
improving hydrologic theory and to better understand and predict the flow of water through catchments. 相似文献
16.
In recent decades, copula functions have been applied in bivariate drought duration and severity frequency analysis. Among several potential copulas, Clayton has been mostly used in drought analysis. In this research, we studied the influence of the tail shape of various copula functions (i.e. Gumbel, Frank, Clayton and Gaussian) on drought bivariate frequency analysis. The appropriateness of Clayton copula for the characterization of drought characteristics is also investigated. Drought data are extracted from standardized precipitation index time series for four stations in Canada (La Tuque and Grande Prairie) and Iran (Anzali and Zahedan). Both duration and severity data sets are positively skewed. Different marginal distributions were first fitted to drought duration and severity data. The gamma and exponential distributions were selected for drought duration and severity, respectively, according to the positive skewness and Kolmogorov–Smirnov test. The results of copula modelling show that the Clayton copula function is not an appropriate choice for the used data sets in the current study and does not give more drought risk information than an independent model for which the duration and severity dependence is not significant. The reason is that the dependence of two variables in the upper tail of Clayton copula is very weak and similar to the independent case, whereas the observed data in the transformed domain of cumulative density function show high association in the upper tail. Instead, the Frank and Gumbel copula functions show better performance than Clayton function for drought bivariate frequency analysis. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
17.
Abstract A procedure is presented for using the bivariate normal distribution to describe the joint distribution of storm peaks (maximum rainfall intensities) and amounts which are mutually correlated. The Box-Cox transformation method is used to normalize original marginal distributions of storm peaks and amounts regardless of the original forms of these distributions. The transformation parameter is estimated using the maximum likelihood method. The joint cumulative distribution function, the conditional cumulative distribution function, and the associated return periods can be readily obtained based on the bivariate normal distribution. The method is tested and validated using two rainfall data sets from two meteorological stations that are located in different climatic regions of Japan. The theoretical distributions show a good fit to observed ones. 相似文献
18.
D. A. Holdsworth Rupa Vuthaluru Iain M. Reid Robert A. Vincent 《Journal of Atmospheric and Solar》2002,64(18)
The differential absorption experiment (DAE) was first proposed in the 1950s for the estimation of mesospheric and lower thermospheric electron density using MF/HF radars. The technique was used extensively until the late 1970s, when interest in the technique declined, due to experimental limitations and questions regarding the assumptions of the technique. This paper describes the application of the DAE within the online observations of the Buckland Park MF (BPMF) radar. The experimental limitations of the technique for the BPMF radar are discussed, with particular attention paid to effects of complex gain differences between receiving channels used to decompose the linearly received signals into circular components. Hourly and monthly averaged midday DAE electron densities are presented, revealing good agreement with IRI model estimates. Monthly averaged midnight DAE electron densities are also presented, revealing good qualitative agreement with the IRI model estimates. 相似文献
19.
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
20.
Ke-Sheng Cheng Ju-Chen Hou Jun-Jih Liou Yii-Chen Wu Jie-Lun Chiang 《Stochastic Environmental Research and Risk Assessment (SERRA)》2011,25(2):107-122
A frequency-factor based approach for stochastic simulation of bivariate gamma distribution is proposed. The approach involves
generation of bivariate normal samples with a correlation coefficient consistent with the correlation coefficient of the corresponding
bivariate gamma samples. Then the bivariate normal samples are transformed to bivariate gamma samples using the well-known
general equation of hydrological frequency analysis. We demonstrate that the proposed bivariate gamma simulation approach
is capable of generating random sample pairs which not only have the desired marginal densities of component random variables
but also their correlation coefficient. Scatter plots of simulated bivariate sample pairs also exhibit appropriate linear
patterns (dependence structure) that are commonly observed in environmental and hydrological applications. Caution should
also be exercised when specifying combinations of coefficients of skewness and the correlation coefficient for bivariate gamma
simulation. 相似文献