Search results for: variogram

Authors: Sheikh Samsuzzhan Alam

Abstract:

The present study investigates the selection of variogram model in analyzing spatial variations of environmental variables with the trend. Sometimes, the autofitted theoretical variogram does not really capture the true nature of the empirical semivariogram. So proper exploration and analysis are needed to select the best variogram model. For this study, an open source data collected from California Soil Resource Lab1 is used to explain the problems when fitting a theoretical variogram. Five most commonly used variogram models: Linear, Gaussian, Exponential, Matern, and Spherical were fitted to the experimental semivariogram. Ordinary kriging methods were considered to evaluate the accuracy of the selected variograms through cross-validation. This study is beneficial for selecting an appropriate theoretical variogram model for environmental variables.

Keywords: anisotropy, cross-validation, environmental variables, kriging, variogram models

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Authors: Hazem Al-Mofleh, John Daniels, Joseph McKean

Abstract:

Within geostatistics research, effective estimation of the variogram points has been examined, particularly in developing robust alternatives. The parametric fit of these variogram points which eventually defines the kriging weights, however, has not received the same attention from a robust perspective. This paper proposes the use of the non-linear Wilcoxon norm over weighted non-linear least squares as a robust variogram fitting alternative. First, we introduce the concept of variogram estimation and fitting. Then, as an alternative to non-linear weighted least squares, we discuss the non-linear Wilcoxon estimator. Next, the robustness properties of the non-linear Wilcoxon are demonstrated using a contaminated spatial data set. Finally, under simulated conditions, increasing levels of contaminated spatial processes have their variograms points estimated and fit. In the fitting of these variogram points, both non-linear Weighted Least Squares and non-linear Wilcoxon fits are examined for efficiency. At all levels of contamination (including 0%), using a robust estimation and robust fitting procedure, the non-weighted Wilcoxon outperforms weighted Least Squares.

Keywords: non-linear wilcoxon, robust estimation, variogram estimation, wilcoxon norm

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Authors: Hazem M. Al-Mofleh, John E. Daniels, Joseph W. McKean

Abstract:

In this paper numerous robust fitting procedures are considered in estimating spatial variograms. In spatial statistics, the conventional variogram fitting procedure (non-linear weighted least squares) suffers from the same outlier problem that has plagued this method from its inception. Even a 3-parameter model, like the variogram, can be adversely affected by a single outlier. This paper uses the Hogg-Type adaptive procedures to select an optimal score function for a rank-based estimator for these non-linear models. Numeric examples and simulation studies will demonstrate the robustness, utility, efficiency, and validity of these estimates.

Keywords: asymptotic relative efficiency, non-linear rank-based, rank estimates, variogram

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Authors: Benbiao Song, Yan Gao, Zhuo Liu

Abstract:

Geostatistical modeling is the key technic for reservoir characterization, the quality of geological models will influence the prediction of reservoir performance greatly, but few studies have been done to quantify the factors impacting geostatistical reservoir modeling accuracy. In this study, 16 fluvial prototype models have been established to represent different geological complexity, 6 cases range from 16 to 361 wells were defined to reproduce all those 16 prototype models by different methodologies including SIS, object-based and MPFS algorithms accompany with different constraint parameters. Modeling accuracy ratio was defined to quantify the influence of each factor, and ten realizations were averaged to represent each accuracy ratio under the same modeling condition and parameters association. Totally 5760 simulations were done to quantify the relative contribution of each factor to the simulation accuracy, and the results can be used as strategy guide for facies modeling in the similar condition. It is founded that data density, geological trend and geological complexity have great impact on modeling accuracy. Modeling accuracy may up to 90% when channel sand width reaches up to 1.5 times of well space under whatever condition by SIS and MPFS methods. When well density is low, the contribution of geological trend may increase the modeling accuracy from 40% to 70%, while the use of proper variogram may have very limited contribution for SIS method. It can be implied that when well data are dense enough to cover simple geobodies, few efforts were needed to construct an acceptable model, when geobodies are complex with insufficient data group, it is better to construct a set of robust geological trend than rely on a reliable variogram function. For object-based method, the modeling accuracy does not increase obviously as SIS method by the increase of data density, but kept rational appearance when data density is low. MPFS methods have the similar trend with SIS method, but the use of proper geological trend accompany with rational variogram may have better modeling accuracy than MPFS method. It implies that the geological modeling strategy for a real reservoir case needs to be optimized by evaluation of dataset, geological complexity, geological constraint information and the modeling objective.

Keywords: fluvial facies, geostatistics, geological trend, modeling strategy, modeling accuracy, variogram

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Authors: Ekrem Canli, Thomas Glade

Abstract:

The precise prediction of rainfall in space and time is a key element to most landslide early warning systems. Unfortunately, the spatial variability of rainfall in many early warning applications is often disregarded. A common simplification is to use uniformly distributed rainfall to characterize aerial rainfall intensity. With spatially differentiated rainfall information, real-time comparison with rainfall thresholds or the implementation in process-based approaches might form the basis for improved landslide warnings. This study suggests an automated workflow from the hourly, web-based collection of rain gauge data to the generation of spatially differentiated rainfall predictions based on kriging. Because the application of kriging is usually a labor intensive task, a simplified and consequently automated variogram modeling procedure was applied to up-to-date rainfall data. The entire workflow was carried out purely with open source technology. Validation results, albeit promising, pointed out the challenges that are involved in pure distance based, automated geostatistical interpolation techniques for ever-changing environmental phenomena over short temporal and spatial extent.

Keywords: kriging, landslide early warning system, spatial rainfall prediction, variogram modelling, web scraping

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Authors: Sachin Jain, Daniel Perez-Astudillo, Dunia A. Bachour, Antonio P. Sanfilippo

Abstract:

The future of solar energy in Qatar is evolving steadily. Hence, high-quality spatial solar radiation data is of the uttermost requirement for any planning and commissioning of solar technology. Generally, two types of solar radiation data are available: satellite data and ground observations. Satellite solar radiation data is developed by the physical and statistical model. Ground data is collected by solar radiation measurement stations. The ground data is of high quality. However, they are limited to distributed point locations with the high cost of installation and maintenance for the ground stations. On the other hand, satellite solar radiation data is continuous and available throughout geographical locations, but they are relatively less accurate than ground data. To utilize the advantage of both data, a product has been developed here which provides spatial continuity and higher accuracy than any of the data alone. The popular satellite databases: National Solar radiation Data Base, NSRDB (PSM V3 model, spatial resolution: 4 km) is chosen here for merging with ground-measured solar radiation measurement in Qatar. The spatial distribution of ground solar radiation measurement stations is comprehensive in Qatar, with a network of 13 ground stations. The monthly average of the daily total Global Horizontal Irradiation (GHI) component from ground and satellite data is used for error analysis. The normalized root means square error (NRMSE) values of 3.31%, 6.53%, and 6.63% for October, November, and December 2019 were observed respectively when comparing in-situ and NSRDB data. The method is based on the Empirical Bayesian Kriging Regression Prediction model available in ArcGIS, ESRI. The workflow of the algorithm is based on the combination of regression and kriging methods. A regression model (OLS, ordinary least square) is fitted between the ground and NSBRD data points. A semi-variogram is fitted into the experimental semi-variogram obtained from the residuals. The kriging residuals obtained after fitting the semi-variogram model were added to NSRBD data predicted values obtained from the regression model to obtain the final predicted values. The NRMSE values obtained after merging are respectively 1.84%, 1.28%, and 1.81% for October, November, and December 2019. One more explanatory variable, that is the ground elevation, has been incorporated in the regression and kriging methods to reduce the error and to provide higher spatial resolution (30 m). The final GHI maps have been created after merging, and NRMSE values of 1.24%, 1.28%, and 1.28% have been observed for October, November, and December 2019, respectively. The proposed merging method has proven as a highly accurate method. An additional method is also proposed here to generate calibrated maps by using regression and kriging model and further to use the calibrated model to generate solar radiation maps from the explanatory variable only when not enough historical ground data is available for long-term analysis. The NRMSE values obtained after the comparison of the calibrated maps with ground data are 5.60% and 5.31% for November and December 2019 month respectively.

Keywords: global horizontal irradiation, GIS, empirical bayesian kriging regression prediction, NSRDB

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Authors: Dedah Ahmed Babou, Nicolas Bez

Abstract:

The Min-Max autocorrelation factor (MAF) approach makes it possible to express in a space formed by spatially independent factors, spatiotemporal observations. These factors are ordered in decreasing order of spatial autocorrelation. The starting observations are thus expressed in the space formed by these factors according to temporal coordinates. Each vector of temporal coefficients expresses the temporal evolution of the weight of the corresponding factor. Applying this approach has enabled us to achieve the following results: (i) Define a spatially orthogonal space in which the projections of the raw data are determined; (ii) Define a limit threshold for the factors with the strongest structures in order to analyze the weight, and the temporal evolution of these different structures (iii) Study the correlation between the temporal evolution of the persistent spatial structures and that of the observed average abundance (iv) Propose prototypes of campaigns reflecting a high vs. low abundance (v) Propose a classification of campaigns that highlights seasonal and/or temporal similarities. These results were obtained by analyzing the octopus yield during the scientific campaigns of the oceanographic vessel Al Awam during the period 1989-2017 in the Mauritanian exclusive economic zone.

Keywords: spatiotemporal , autocorrelation, kriging, variogram, Octopus vulgaris

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