排序方式： 共有23条查询结果，搜索用时 31 毫秒
1.
Pardo-Igúzquiza Eulogio Dowd Peter A. Rizo-Decelis Luis David 《Mathematical Geosciences》2020,52(5):639-650
Mathematical Geosciences - The universality of fractals implies that very different physical processes can give rise to similar complex spatial patterns. Sinkholes (dolines) and galaxies provide a... 相似文献
2.
Compositional Bayesian indicator estimation 总被引：1，自引：1，他引：0
Carolina Guardiola-Albert Eulogio Pardo-Ig��zquiza 《Stochastic Environmental Research and Risk Assessment (SERRA)》2011,25(6):835-849
Indicator kriging is widely used for mapping spatial binary variables and for estimating the global and local spatial distributions
of variables in geosciences. For continuous random variables, indicator kriging gives an estimate of the cumulative distribution
function, for a given threshold, which is then the estimate of a probability. Like any other kriging procedure, indicator
kriging provides an estimation variance that, although not often used in applications, should be taken into account as it
assesses the uncertainty of the estimate. An alternative approach to indicator estimation is proposed in this paper. In this
alternative approach the complete probability density function of the indicator estimate is evaluated. The procedure is described
in a Bayesian framework, using a multivariate Gaussian likelihood and an a priori distribution which are both combined according
to Bayes theorem in order to obtain a posterior distribution for the indicator estimate. From this posterior distribution,
point estimates, interval estimates and uncertainty measures can be obtained. Among the point estimates, the median of the
posterior distribution is the maximum entropy estimate because there is a fifty-fifty chance of the unknown value of the estimate
being larger or smaller than the median; that is, there is maximum uncertainty in the choice between two alternatives. Thus
in some sense, the latter is an indicator estimator, alternative to the kriging estimator, that includes its own uncertainty.
On the other hand, the mode of the posterior distribution estimator, assuming a uniform prior, is coincidental with the simple
kriging estimator. Additionally, because the indicator estimate can be considered as a two-part composition which domain of
definition is the simplex, the method is extended to compositional Bayesian indicator estimation. Bayesian indicator estimation
and compositional Bayesian indicator estimation are illustrated with an environmental case study in which the probability
of the content of a geochemical element in soil being over a particular threshold is of interest. The computer codes and its
user guides are public domain and freely available. 相似文献
3.
Spatiotemporal estimation of snow depth using point data from snow stakes,digital terrain models,and satellite data 
下载免费PDF全文
下载免费PDF全文 Antonio‐Juan Collados‐Lara Eulogio Pardo‐Igúzquiza David Pulido‐Velazquez 《水文研究》2017,31(10):1966-1982
Snow availability in Alpine catchments plays an important role in water resources management. In this paper, we propose a method for an optimal estimation of snow depth (areal extension and thickness) in Alpine systems from point data and satellite observations by using significant explanatory variables deduced from a digital terrain model. It is intended to be a parsimonious approach that may complement physical‐based methodologies. Different techniques (multiple regression, multicriteria analysis, and kriging) are integrated to address the following issues: We identify the explanatory variables that could be helpful on the basis of a critical review of the scientific literature. We study the relationship between ground observations and explanatory variables using a systematic procedure for a complete multiple regression analysis. Multiple regression models are calibrated combining all suggested model structures and explanatory variables. We also propose an evaluation of the models (using indices to analyze the goodness of fit) and select the best approaches (models and variables) on the basis of multicriteria analysis. Estimation of the snow depth is performed with the selected regression models. The residual estimation is improved by applying kriging in cases with spatial correlation. The final estimate is obtained by combining regression and kriging results, and constraining the snow domain in accordance with satellite data. The method is illustrated using the case study of the Sierra Nevada mountain range (Southern Spain). A cross‐validation experiment has confirmed the efficiency of the proposed procedure. Finally, although it is not the scope of this work, the snow depth is used to asses a first estimation of snow water equivalent resources. 相似文献
4.
Geostatistical estimation (kriging) and geostatistical simulation are routinely used in ground water hydrology for optimal spatial interpolation and Monte Carlo risk assessment, respectively. Both techniques are based on a model of spatial variability (semivariogram or covariance) that generally is not known but must be inferred from the experimental data. Where the number of experimental data is small (say, several tens), as is not unusual in ground water hydrology, the model fitted to the empirical semivariogram entails considerable uncertainty. If all the practical results are based on this unique fitted model, the final results will be biased. We propose that, instead of using a unique semivariogram model, the full range of models that are inside a given confidence region should be used, and the weight that each semivariogram model has on the final result should depend on its plausibility. The first task, then, is to evaluate the uncertainty of the model, which can be efficiently done by using maximum likelihood inference. The second task is to use the range of plausible models in applications and to show the effect observed on the final results. This procedure is put forth here with kriging and simulation applications, where the uncertainty in semivariogram parameters is propagated into the final results (e.g., the prediction of ground water head). A case study using log-transmissivity data from the Vega de Granada aquifer, in southern Spain, is given to illustrate the methodology. 相似文献
5.
Eulogio?Pardo-Igúzquiza Pedro?Martínez-SantosEmail author Miguel?Martín-Loeches 《Stochastic Environmental Research and Risk Assessment (SERRA)》2018,32(8):2433-2444
This paper deals with the design of optimal spatial sampling of water quality variables in remote regions, where logistics are complicated and the optimization of monitoring networks may be critical to maximize the effectiveness of human and material resources. A methodology that combines the probability of exceeding some particular thresholds with a measurement of the information provided by each pair of experimental points has been introduced. This network optimization concept, where the basic unit of information is not a single spatial location but a pair of spatial locations, is used to emphasize the locations with the greatest information, which are those at the border of the phenomenon (for example contamination or a quality variable exceeding a given threshold), that is, where the variable at one of the locations in the pair is above the threshold value and the other is below the threshold. The methodology is illustrated with a case of optimizing the monitoring network by optimal selection of the subset that best describes the information provided by an exhaustive survey done at a given moment in time but which cannot be repeated systematically due to time or economic constrains. 相似文献
6.
Mathematical Geosciences - Fractal analysis has, for some time, been used to evaluate the roughness of both natural and engineered surfaces. Since the introduction of fractal geometry, evidence of... 相似文献
7.
Empirical Maximum Likelihood Kriging: The General Case 总被引：4，自引：0，他引：4
Although linear kriging is a distribution-free spatial interpolator, its efficiency is maximal only when the experimental data follow a Gaussian distribution. Transformation of the data to normality has thus always been appealing. The idea is to transform the experimental data to normal scores, krige values in the “Gaussian domain” and then back-transform the estimates and uncertainty measures to the “original domain.” An additional advantage of the Gaussian transform is that spatial variability is easier to model from the normal scores because the transformation reduces effects of extreme values. There are, however, difficulties with this methodology, particularly, choosing the transformation to be used and back-transforming the estimates in such a way as to ensure that the estimation is conditionally unbiased. The problem has been solved for cases in which the experimental data follow some particular type of distribution. In general, however, it is not possible to verify distributional assumptions on the basis of experimental histograms calculated from relatively few data and where the uncertainty is such that several distributional models could fit equally well. For the general case, we propose an empirical maximum likelihood method in which transformation to normality is via the empirical probability distribution function. Although the Gaussian domain simple kriging estimate is identical to the maximum likelihood estimate, we propose use of the latter, in the form of a likelihood profile, to solve the problem of conditional unbiasedness in the back-transformed estimates. Conditional unbiasedness is achieved by adopting a Bayesian procedure in which the likelihood profile is the posterior distribution of the unknown value to be estimated and the mean of the posterior distribution is the conditionally unbiased estimate. The likelihood profile also provides several ways of assessing the uncertainty of the estimation. Point estimates, interval estimates, and uncertainty measures can be calculated from the posterior distribution. 相似文献
8.
Monitoring and estimation of snow depth in alpine catchments is needed for a proper assessment of management alternatives for water supply in these water resources systems. The distribution of snowpack thickness is usually approached by using field data that come from snow samples collected at a given number of locations that constitute the monitoring network. Optimal design of this network is required to obtain the best possible estimates. Assuming that there is an existing monitoring network, its optimization may imply the selection of an optimal network as a subset of the existing one (if there are no funds to maintain them) or enlarging the existing network by one or more stations (optimal augmentation problem). We propose an optimization procedure that minimizes the total variance in the estimate of snowpack thickness. The novelty of this work is to treat, for the first time, the problem of snow observation network optimization for an entire mountain range rather than for small catchments as done in the previous studies. Taking into account the reduced data available, which is a common problem in many mountain ranges, the importance of a proper design of these observation networks is even larger. Snowpack thickness is estimated by combining regression models to approach the effect of the explanatory variables and kriging techniques to consider the influence of the stakes location. We solve the optimization problems under different hypotheses, studying the impacts of augmentation and reduction, both, one by one and in pairs. We also analyse the sensitivity of results to nonsnow measurements deduced from satellite information. Finally, we design a new optimal network by combining the reduction and augmentation methods. The methodology has been applied to the Sierra Nevada mountain range (southern Spain), where very limited resources are employed to monitor snowfall and where an optimal snow network design could prove critical. An optimal snow observation network is defined by relocating some observation points. It would reduce the estimation variance by around 600 cm2 (15%). 相似文献
9.
Generalized Bootstrap Method for Assessment of?Uncertainty in Semivariogram Inference 总被引：1，自引：0，他引：1
The semivariogram and its related function, the covariance, play a central role in classical geostatistics for modeling the average continuity of spatially correlated attributes. Whereas all methods are formulated in terms of the true semivariogram, in practice what can be used are estimated semivariograms and models based on samples. A generalized form of the bootstrap method to properly model spatially correlated data is used to advance knowledge about the reliability of empirical semivariograms and semivariogram models based on a single sample. Among several methods available to generate spatially correlated resamples, we selected a method based on the LU decomposition and used several examples to illustrate the approach. The first one is a synthetic, isotropic, exhaustive sample following a normal distribution, the second example is also a synthetic but following a non-Gaussian random field, and a third empirical sample consists of actual raingauge measurements. Results show wider confidence intervals than those found previously by others with inadequate application of the bootstrap. Also, even for the Gaussian example, distributions for estimated semivariogram values and model parameters are positively skewed. In this sense, bootstrap percentile confidence intervals, which are not centered around the empirical semivariogram and do not require distributional assumptions for its construction, provide an achieved coverage similar to the nominal coverage. The latter cannot be achieved by symmetrical confidence intervals based on the standard error, regardless if the standard error is estimated from a parametric equation or from bootstrap. 相似文献
10.
Eulogio Pardo-Igúzquiza 《Mathematical Geology》1999,31(1):47-65
This paper shows the application of the Bayesian inference approach in estimating spatial covariance parameters. This methodology is particularly valuable where the number of experimental data is small, as occurs frequently in modeling reservoirs in petroleum engineering or when dealing with hydrodynamic variables in groundwater hydrology. There are two main advantages of Bayesian estimation: firstly that the complete distribution of the parameters is estimated and, from this distribution, it is a straightforward procedure to obtain point estimates, confidence regions, and interval estimates; secondly, all the prior information about the parameters (information available before the data are collected) is included in the inference procedure through their prior distribution. The results obtained from simulation studies are discussed. 相似文献