共查询到20条相似文献，搜索用时 15 毫秒
1.
A consistent approach to the frequency analysis of hydrologic data in arid and semiarid regions, i.e. the data series containing several zero values (e.g. monthly precipitation in dry seasons, annual peak flow discharges, etc.), requires using discontinuous probability distribution functions. Such an approach has received relatively limited attention. Along the lines of physically based models, the extensions of the Muskingum‐based models to three parameter forms are considered. Using 44 peak flow series from the USGS data bank, the fitting ability of four three‐parameter models was investigated: (1) the Dirac delta combined with Gamma distribution; (2) the Dirac delta combined with two‐parameter generalized Pareto distribution; (3) the Dirac delta combined with two‐parameter Weibull (DWe) distribution; (4) the kinematic diffusion with one additional parameter that controls the probability of the zero event (KD3). The goodness of fit of the models was assessed and compared both by evaluation of discrepancies between the results of both estimation methods (i.e. the method of moments (MOM) and the maximum likelihood method (MLM)) and using the log of likelihood function as a criterion. In most cases, the DWe distribution with MLM‐estimated parameters showed the best fit of all the three‐parameter models. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
2.
叠前反演的目的是基于弹性波理论从地震数据中获得地层参数的可靠估计,进而用于描述地层的流体和岩性特征.然而叠前反演问题都是高维的和非适定的,并且容易受各种噪声和采集过程中不确定因素的影响,因此,为了获得稳定可靠的解必需对反演过程加以合理的约束.本文提出了一种基于非线性二次规划的叠前三参数反演方法.首先基于贝叶斯参数估计理论,假设似然函数服从高斯分布,并使待反演的参数服从于改进的Cauchy分布,从而提高了反演结果的分辨率;其次用协方差矩阵来描述参数间的相关程度,进一步提高了反演结果的稳定性;最后将问题转化为一个非线性二次规划的求解问题,并在多种约束下得到问题的解.仿真实验和实际应用皆已表明,本文提出的反演方法运算速度快捷,既使在信噪比很低的情况下也可获得较好的反演结果,为储层的进一步识别提供更多的物性参数. 相似文献
3.
F. FOURNIER 《水文科学杂志》2013,58(4):521-525
ABSTRACT The extreme value type III distribution was derived by using the principle of maximum entropy. The derivation required only two constraints to be determined from data, and yielded a procedure for estimation of distribution parameters. This method of parameter estimation was comparable to the methods of moments (MOM) and maximum likelihood estimation (MLE) for the low flow data used. 相似文献
4.
S. E. Ahn C. S. Park H. M. Kim 《Stochastic Environmental Research and Risk Assessment (SERRA)》2007,21(6):711-716
This paper is intended to compare the hazard rate from the Bayesian approach with the hazard rate from the maximum likelihood
estimate (MLE) method. The MLE of a parameter is appropriate as long as there are sufficient data. For various reasons, however,
sufficient data may not be available, which may make the result of the MLE method unreliable. In order to resolve the problem,
it is necessary to rely on judgment about unknown parameters. This is done by adopting the Bayesian approach. The hazard rate
of a mixture model can be inferred from a method called Bayesian estimation. For eliciting a prior distribution which can
be used in deriving a Bayesian estimate, a computerized-simulation method is introduced. Finally, a numerical example is given
to illustrate the potential benefits of the Bayesian approach. 相似文献
5.
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
6.
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
7.
8.
Application of distributed hydrological models for predictions in ungauged basins: a method to quantify predictive uncertainty 
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下载免费PDF全文 Stream flow predictions in ungauged basins are one of the most challenging tasks in surface water hydrology because of nonavailability of data and system heterogeneity. This study proposes a method to quantify stream flow predictive uncertainty of distributed hydrologic models for ungauged basins. The method is based on the concepts of deriving probability distribution of model's sensitive parameters by using measured data from a gauged basin and transferring the distribution to hydrologically similar ungauged basins for stream flow predictions. A Monte Carlo simulation of the hydrologic model using sampled parameter sets with assumed probability distribution is conducted. The posterior probability distributions of the sensitive parameters are then computed using a Bayesian approach. In addition, preselected threshold values of likelihood measure of simulations are employed for sizing the parameter range, which helps reduce the predictive uncertainty. The proposed method is illustrated through two case studies using two hydrologically independent sub‐basins in the Cedar Creek watershed located in Texas, USA, using the Soil and Water Assessment Tool (SWAT) model. The probability distribution of the SWAT parameters is derived from the data from one of the sub‐basins and is applied for simulation in the other sub‐basin considered as pseudo‐ungauged. In order to assess the robustness of the method, the numerical exercise is repeated by reversing the gauged and pseudo‐ungauged basins. The results are subsequently compared with the measured stream flow from the sub‐basins. It is observed that the measured stream flow in the pseudo‐ungauged basin lies well within the estimated confidence band of predicted stream flow. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
9.
V. P. Singh H. Guo 《Stochastic Environmental Research and Risk Assessment (SERRA)》1997,11(3):211-227
The principle of maximum entropy (POME) was employed to derive a new method of parameter estimation for the 2-parameter generalized
Pareto (GP2) distribution. Monte Carlo simulated data were used to evaluate this method and compare it with the methods of
moments (MOM), probability weighted moments (PWM), and maximum likelihood estimation (MLE). The parameter estimates yielded
by POME were comparable or better within certain ranges of sample size and coefficient of variation. 相似文献
10.
J.-H. Heo J. D. Salas K.-D. Kim 《Stochastic Environmental Research and Risk Assessment (SERRA)》2001,15(4):284-309
Estimation of confidence limits and intervals for the two- and three-parameter Weibull distributions are presented based
on the methods of moment (MOM), probability weighted moments (PWM), and maximum likelihood (ML). The asymptotic variances
of the MOM, PWM, and ML quantile estimators are derived as a function of the sample size, return period, and parameters. Such
variances can be used for estimating the confidence limits and confidence intervals of the population quantiles. Except for
the two-parameter Weibull model, the formulas obtained do not have simple forms but can be evaluated numerically. Simulation
experiments were performed to verify the applicability of the derived confidence intervals of quantiles. The results show
that overall, the ML method for estimating the confidence limits performs better than the other two methods in terms of bias
and mean square error. This is specially so for γ≥0.5 even for small sample sizes (e.g. N=10). However, the drawback of the ML method for determining the confidence limits is that it requires that the shape parameter
be bigger than 2. The Weibull model based on the MOM, ML, and PWM estimation methods was applied to fit the distribution of
annual 7-day low flows and 6-h maximum annual rainfall data. The results showed that the differences in the estimated quantiles
based on the three methods are not large, generally are less than 10%. However, the differences between the confidence limits
and confidence intervals obtained by the three estimation methods may be more significant. For instance, for the 7-day low
flows the ratio between the estimated confidence interval to the estimated quantile based on ML is about 17% for T≥2 while it is about 30% for estimation based on MOM and PWM methods. In addition, the analysis of the rainfall data using
the three-parameter Weibull showed that while ML parameters can be estimated, the corresponding confidence limits and intervals
could not be found because the shape parameter was smaller than 2. 相似文献
11.
Estimation of soil hydraulic properties and their uncertainty through the Beerkan infiltration experiment 下载免费PDF全文
下载免费PDF全文 The Beerkan method based on in situ single‐ring water infiltration experiments along with the relevant specific Beerkan estimation of soil transfer parameters (BEST) algorithm is attractive for simple soil hydraulic characterization. However, the BEST algorithm may lead to erroneous or null values for the saturated hydraulic conductivity and sorptivity especially when there are only few infiltration data points under the transient flow state, either for sandy soil or soils in wet conditions. This study developed an alternative algorithm for analysis of the Beerkan infiltration experiment referred to as BEST‐generalized likelihood uncertainty estimation (GLUE). The proposed method estimates the scale parameters of van Genuchten water retention and Brooks–Corey hydraulic conductivity functions through the GLUE methodology. The GLUE method is a Bayesian Monte Carlo parameter estimation technique that makes use of a likelihood function to measure the goodness‐of‐fit between modelled and observed data. The results showed that using a combination of three different likelihood measurements based on observed transient flow, steady‐state flow and experimental steady‐state infiltration rate made the BEST‐GLUE procedure capable of performing an efficient inverse analysis of Beerkan infiltration experiments. Therefore, it is more applicable for a wider range of soils with contrasting texture, structure, and initial and saturated water content. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
12.
Large observed datasets are not stationary and/or depend on covariates, especially, in the case of extreme hydrometeorological variables. This causes the difficulty in estimation, using classical hydrological frequency analysis. A number of non-stationary models have been developed using linear or quadratic polynomial functions or B-splines functions to estimate the relationship between parameters and covariates. In this article, we propose regularised generalized extreme value model with B-splines (GEV-B-splines models) in a Bayesian framework to estimate quantiles. Regularisation is based on penalty and aims to favour parsimonious model especially in the case of large dimension space. Penalties are introduced in a Bayesian framework and the corresponding priors are detailed. Five penalties are considered and the corresponding priors are developed for comparison purpose as: Least absolute shrinkage and selection (Lasso and Ridge) and smoothing clipped absolute deviations (SCAD) methods (SCAD1, SCAD2 and SCAD3). Markov chain Monte Carlo (MCMC) algorithms have been developed for each model to estimate quantiles and their posterior distributions. Those approaches are tested and illustrated using simulated data with different sample sizes. A first simulation was made on polynomial B-splines functions in order to choose the most efficient model in terms of relative mean biais (RMB) and the relative mean-error (RME) criteria. A second simulation was performed with the SCAD1 penalty for sinusoidal dependence to illustrate the flexibility of the proposed approach. Results show clearly that the regularized approaches leads to a significant reduction of the bias and the mean square error, especially for small sample sizes (n < 100). A case study has been considered to model annual peak flows at Fort-Kent catchment with the total annual precipitations as covariates. The conditional quantile curves were given for the regularized and the maximum likelihood methods. 相似文献
13.
Selection of the best fit flood frequency distribution and parameter estimation procedure: a case study for Tasmania in Australia 总被引：1，自引：1，他引：0
Khaled Haddad Ataur Rahman 《Stochastic Environmental Research and Risk Assessment (SERRA)》2011,25(3):415-428
Selection of a flood frequency distribution and associated parameter estimation procedure is an important step in flood frequency
analysis. This is however a difficult task due to problems in selecting the best fit distribution from a large number of candidate
distributions and parameter estimation procedures available in the literature. This paper presents a case study with flood
data from Tasmania in Australia, which examines four model selection criteria: Akaike Information Criterion (AIC), Akaike
Information Criterion—second order variant (AICc), Bayesian Information Criterion (BIC) and a modified Anderson–Darling Criterion (ADC). It has been found from the Monte
Carlo simulation that ADC is more successful in recognizing the parent distribution correctly than the AIC and BIC when the
parent is a three-parameter distribution. On the other hand, AIC and BIC are better in recognizing the parent distribution
correctly when the parent is a two-parameter distribution. From the seven different probability distributions examined for
Tasmania, it has been found that two-parameter distributions are preferable to three-parameter ones for Tasmania, with Log
Normal appears to be the best selection. The paper also evaluates three most widely used parameter estimation procedures for
the Log Normal distribution: method of moments (MOM), method of maximum likelihood (MLE) and Bayesian Markov Chain Monte Carlo
method (BAY). It has been found that the BAY procedure provides better parameter estimates for the Log Normal distribution,
which results in flood quantile estimates with smaller bias and standard error as compared to the MOM and MLE. The findings
from this study would be useful in flood frequency analyses in other Australian states and other countries in particular,
when selecting an appropriate probability distribution from a number of alternatives. 相似文献
14.
Mahyar Shafii Bryan Tolson Loren Shawn Matott 《Stochastic Environmental Research and Risk Assessment (SERRA)》2014,28(6):1493-1510
This study compares formal Bayesian inference to the informal generalized likelihood uncertainty estimation (GLUE) approach for uncertainty-based calibration of rainfall-runoff models in a multi-criteria context. Bayesian inference is accomplished through Markov Chain Monte Carlo (MCMC) sampling based on an auto-regressive multi-criteria likelihood formulation. Non-converged MCMC sampling is also considered as an alternative method. These methods are compared along multiple comparative measures calculated over the calibration and validation periods of two case studies. Results demonstrate that there can be considerable differences in hydrograph prediction intervals generated by formal and informal strategies for uncertainty-based multi-criteria calibration. Also, the formal approach generates definitely preferable validation period results compared to GLUE (i.e., tighter prediction intervals that show higher reliability) considering identical computational budgets. Moreover, non-converged MCMC (based on the standard Gelman–Rubin metric) performance is reasonably consistent with those given by a formal and fully-converged Bayesian approach even though fully-converged results requires significantly larger number of samples (model evaluations) for the two case studies. Therefore, research to define alternative and more practical convergence criteria for MCMC applications to computationally intensive hydrologic models may be warranted. 相似文献
15.
In this study, we adopt an improved Bayesian approach based on free-knot B-spline bases to study the spatial and temporal distribution of the b-value. Synthetic tests show that the improved Bayesian approach has a superior performance compared to the Bayesian approach as well as the widely used maximum likelihood estimation (MLE) method in fitting the real variation of b-values. We then apply the improved Bayesian approach to North China and find that the b-value has a clear relevance to seismicity. Temporal changes of b-values are also investigated in two specific areas of North China. We interpret sharp decreases in the b-values as useful messages in earthquake hazard analysis. 相似文献
16.
One‐dimensional flow simulations were conducted at four locations of the shallow alluvial aquifer of the upper Rhine River (at the Erstein polder) to quantify the time‐dependent moisture distribution, the water flux and the water volume infiltrated in the unsaturated zone as a function of soil heterogeneities during a five‐day‐long flooding event. Three methods of estimating the hydraulic parameters of soil in the vadose zone were tested. They are based on the following: (1) experimental data, (2) soil particle‐size distribution and (3) pedology information on soils. Water fluxes calculated from modelling approaches 2 and 3 were compared with those of the experiment‐based values and the effect of these differences on the arrival time and velocity of water at the water table were analysed. Major differences in water fluxes were found among the methods of estimating the hydrodynamic parameters. At the Terrace location, the groundwater recharge predicted using soil data from methods 1 and 2 are approximately 4500 and 2400 mm, respectively. Flow simulations using soil data and the experiment‐based method show the highest velocities of infiltrating water at the soil surface and largest volume of groundwater infiltration but result in the lowest centres of the moisture content mass. The results obtained using soil data based on the pedological method are similar to those calculated using soil parameters based on the particle‐size distribution of extracted soil samples. Water pressure profiles calculated on Terrace and Channel location, 3 and 7 days after the inundation event agreed reasonably well with those observed when using hydrodynamic parameters from the experiment‐based method. However, the flow model using the pedology‐based parameters largely underestimates the time needed to achieve hydrostatic conditions of the soil water profile once water flooding at the soil surface stops. This can be mainly attributed to the low values of estimated van Genuchten parameter α. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
17.
This paper investigates the suitability of a three-parameter (scale, shape, and location) Weibull distribution in probabilistic assessment of earthquake hazards. The performance is also compared with two other popular models from same Weibull family, namely the two-parameter Weibull model and the inverse Weibull model. A complete and homogeneous earthquake catalog (Yadav et al. in Pure Appl Geophys 167:1331–1342, 2010) of 20 events (M ≥ 7.0), spanning the period 1846 to 1995 from north–east India and its surrounding region (20°–32°N and 87°–100°E), is used to perform this study. The model parameters are initially estimated from graphical plots and later confirmed from statistical estimations such as maximum likelihood estimation (MLE) and method of moments (MoM). The asymptotic variance–covariance matrix for the MLE estimated parameters is further calculated on the basis of the Fisher information matrix (FIM). The model suitability is appraised using different statistical goodness-of-fit tests. For the study area, the estimated conditional probability for an earthquake within a decade comes out to be very high (≥0.90) for an elapsed time of 18 years (i.e., 2013). The study also reveals that the use of location parameter provides more flexibility to the three-parameter Weibull model in comparison to the two-parameter Weibull model. Therefore, it is suggested that three-parameter Weibull model has high importance in empirical modeling of earthquake recurrence and seismic hazard assessment. 相似文献
18.
地震时间分布特征研究是进行地震预测和地震危险性分析的重要基础。以中国海域统一地震目录为基础资料，以指数分布模型、伽马分布模型、威布尔分布模型、对数正态分布模型以及布朗过程时间分布（BPT）模型为目标模型，采用极大似然法估算模型参数。根据赤池信息准则（AIC）、贝叶斯信息准则（BIC）以及K-S检验结果确定能够描述海域地震时间分布的最优模型。结果表明，对于震级相对较小（ M <6）的地震，指数分布、伽马分布以及威布尔分布均能较好地描述其时间分布特征；在大的区域范围内（如整个海域），震级相对较大（ M >6）的地震可完全采用指数分布描述其时间分布特征；在较小的区域范围内（如地震带），大地震时间间隔可能更加符合对数正态分布和BPT分布。此外，文中还采用扩散熵分析法研究地震之间的丛集性和时间相关性，结果表明，地震活动存在长期记忆性，震级相对较小（ M <6）的地震受更大地震的影响，从而在时间上表现出丛集特征。本文的研究结果对地震预测、地震危险性计算中地震时间分布模型选择和地震活动性参数计算具有一定参考价值，对理解地震孕育发生机理具有一定科学意义。 相似文献
19.
Stationarity is often assumed for frequency analysis of low flows in water resources management and planning. However, many studies have shown that flow characteristics, particularly the frequency spectrum of extreme hydrologic events, were modified by climate change and human activities. Thus, the conventional frequency analysis that fails to consider the nonstationary characteristics may lead to costly design. The analysis presented in this paper was based on the more than 100 years of daily flow data from the Yichang gauging station 44 km downstream of the Three Gorges Dam. The Mann–Kendall trend test under the scaling hypothesis showed that the annual low flows had a significant monotonic trend, whereas an abrupt change point was identified in 1936 by the Pettitt test. The climate‐informed low‐flow frequency analysis and the divided and combined method were employed to account for the impacts from related climate variables and nonstationarities in annual low flows. Without prior knowledge of the probability density function for the gauging station, six distribution functions including the generalized extreme values (GEV), Pearson Type III, Gumbel, Gamma, Lognormal and Weibull distributions have been tested to find the best fit, in which the local likelihood method is used to estimate the parameters. Analyses show that GEV had the best fit for the observed low flows. This study has also shown that the climate‐informed low‐flow frequency analysis is able to exploit the link between climate indices and low flows, which would account for the dynamic feature for reservoir management and provide more accurate and reliable designs for infrastructure and water supply. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
20.
Application of L‐moments and Bayesian inference for low‐flow regionalization in Sefidroud basin,Iran 下载免费PDF全文
下载免费PDF全文 Reliable estimation of low flows at ungauged catchments is one of the major challenges in water‐resources planning and management. This study aims at providing at‐site and ungauged sites low‐flow frequency analysis using regionalization approach. A two‐stage delineating homogeneous region is proposed in this study. Clustering sites with similar low‐flow L‐moment ratios is initially conducted, and L‐moment‐based discordancy and heterogeneity measures are then used to detect unusual sites. Based on the goodness‐of‐fit test statistic, the best‐fit regional model is identified in each hydrologically homogeneous region. The relationship between mean annual 7‐day minimum flow and hydro‐geomorphic characteristics is also constructed in each homogeneous region associated with the derived regional model for estimating various low‐flow quantiles at ungauged sites. Uncertainty analysis of model parameters and low‐flow estimations is carried out using the Bayesian inference. Applied in Sefidroud basin located in northwestern Iran, two hydrologically homogeneous regions are identified, i.e. the east and west regions. The best‐fit regional model for the east and west regions are generalized logistic and Pearson type III distributions, respectively. The results show that the proposed approach provides reasonably good accuracy for at‐site as well as ungauged‐site frequency analysis. Besides, interval estimations for model parameters and low flows provide uncertainty information, and the results indicate that Bayesian confidence intervals are significantly reduced when comparing with the outcomes of conventional t‐distribution method. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献