Spatial modeling is increasingly prominent in many fields of science as statisticians attempt to characterize variability of the processes that are spatially indexed. This paper shows that the Gaussian random field framework is useful for characterizing spatial statistics for soil properties. A sample of soil properties in 94 spatial locations are taken from a field (186.35m×211.44m) wide in northern Ethiopia, Karsa-Malima. We use observations of organic carbon (OC) from the site in our study. Box-Cox transformation is used because of OC follows non-Gaussian distributions. We develop ordinary kriging which is universal kriging with unknown trend models which enables us to predict any point within the field even outside the field up to the “Range” of the model. In this thesis work we predict 100×100 grids (10000 points) using kriging interpolation models. More over in each of these 10000 locations 1000 conditional simulations are made. Interestingly prediction using universal kriging and mean of conditional simulations agree in expectation and kriging variance. For covariance and/or variogram modeling and for parameter estimation we used least square principle and maximum likelihood estimation method. The classical geostatistical approach known as kriging is used as a spatial model for spatial prediction with associated spatial variances. Moreover, conditional simulation is performed. From ordinary kriging model results, predictions are accurate when predictions are close to observation locations. Prediction variance in the observed locations is close to the nugget effect.
| Published in | American Journal of Theoretical and Applied Statistics (Volume 8, Issue 6) |
| DOI | 10.11648/j.ajtas.20190806.21 |
| Page(s) | 296-305 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2019. Published by Science Publishing Group |
Gaussian Random Fields, Kriging, Interpolation, Variogram, Range
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APA Style
Tofik Mussa Reshid. (2019). Kriging and Simulation in Gaussian Random Fields Applied to Soil Property Interpolation. American Journal of Theoretical and Applied Statistics, 8(6), 296-305. https://doi.org/10.11648/j.ajtas.20190806.21
ACS Style
Tofik Mussa Reshid. Kriging and Simulation in Gaussian Random Fields Applied to Soil Property Interpolation. Am. J. Theor. Appl. Stat. 2019, 8(6), 296-305. doi: 10.11648/j.ajtas.20190806.21
AMA Style
Tofik Mussa Reshid. Kriging and Simulation in Gaussian Random Fields Applied to Soil Property Interpolation. Am J Theor Appl Stat. 2019;8(6):296-305. doi: 10.11648/j.ajtas.20190806.21
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Download@article{10.11648/j.ajtas.20190806.21,
author = {Tofik Mussa Reshid},
title = {Kriging and Simulation in Gaussian Random Fields Applied to Soil Property Interpolation},
journal = {American Journal of Theoretical and Applied Statistics},
volume = {8},
number = {6},
pages = {296-305},
doi = {10.11648/j.ajtas.20190806.21},
url = {https://doi.org/10.11648/j.ajtas.20190806.21},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20190806.21},
abstract = {Spatial modeling is increasingly prominent in many fields of science as statisticians attempt to characterize variability of the processes that are spatially indexed. This paper shows that the Gaussian random field framework is useful for characterizing spatial statistics for soil properties. A sample of soil properties in 94 spatial locations are taken from a field (186.35m×211.44m) wide in northern Ethiopia, Karsa-Malima. We use observations of organic carbon (OC) from the site in our study. Box-Cox transformation is used because of OC follows non-Gaussian distributions. We develop ordinary kriging which is universal kriging with unknown trend models which enables us to predict any point within the field even outside the field up to the “Range” of the model. In this thesis work we predict 100×100 grids (10000 points) using kriging interpolation models. More over in each of these 10000 locations 1000 conditional simulations are made. Interestingly prediction using universal kriging and mean of conditional simulations agree in expectation and kriging variance. For covariance and/or variogram modeling and for parameter estimation we used least square principle and maximum likelihood estimation method. The classical geostatistical approach known as kriging is used as a spatial model for spatial prediction with associated spatial variances. Moreover, conditional simulation is performed. From ordinary kriging model results, predictions are accurate when predictions are close to observation locations. Prediction variance in the observed locations is close to the nugget effect.},
year = {2019}
}
TY - JOUR T1 - Kriging and Simulation in Gaussian Random Fields Applied to Soil Property Interpolation AU - Tofik Mussa Reshid Y1 - 2019/12/30 PY - 2019 N1 - https://doi.org/10.11648/j.ajtas.20190806.21 DO - 10.11648/j.ajtas.20190806.21 T2 - American Journal of Theoretical and Applied Statistics JF - American Journal of Theoretical and Applied Statistics JO - American Journal of Theoretical and Applied Statistics SP - 296 EP - 305 PB - Science Publishing Group SN - 2326-9006 UR - https://doi.org/10.11648/j.ajtas.20190806.21 AB - Spatial modeling is increasingly prominent in many fields of science as statisticians attempt to characterize variability of the processes that are spatially indexed. This paper shows that the Gaussian random field framework is useful for characterizing spatial statistics for soil properties. A sample of soil properties in 94 spatial locations are taken from a field (186.35m×211.44m) wide in northern Ethiopia, Karsa-Malima. We use observations of organic carbon (OC) from the site in our study. Box-Cox transformation is used because of OC follows non-Gaussian distributions. We develop ordinary kriging which is universal kriging with unknown trend models which enables us to predict any point within the field even outside the field up to the “Range” of the model. In this thesis work we predict 100×100 grids (10000 points) using kriging interpolation models. More over in each of these 10000 locations 1000 conditional simulations are made. Interestingly prediction using universal kriging and mean of conditional simulations agree in expectation and kriging variance. For covariance and/or variogram modeling and for parameter estimation we used least square principle and maximum likelihood estimation method. The classical geostatistical approach known as kriging is used as a spatial model for spatial prediction with associated spatial variances. Moreover, conditional simulation is performed. From ordinary kriging model results, predictions are accurate when predictions are close to observation locations. Prediction variance in the observed locations is close to the nugget effect. VL - 8 IS - 6 ER -
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