Kriging in the Presence of Locally Varying Anisotropy Using Non-Euclidean Distances

Boisvert, Jeff B.; Manchuk, John G.; Deutsch, Clayton V.

doi:10.1007/s11004-009-9229-1

Cited by 65 publications

(39 citation statements)

References 13 publications

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“…Therefore, the incorporation of this type of spatial anisotropy in the model will allow for greater accuracy in the construction of thematic maps that describe the spatial variability of the phenomenon under study. There are studies in the literature describing in detail the concept of anisotropy and the construction of anisotropic spatial models (Zimmerman, 1993;Chorti and Hristopulos, 2008;Guedes et al, 2008;Boisvert et al, 2009;Facas et al, 2010). However, the main difficulty of the researchers on the use of anisotropic spatial models focuses on defining the importance of estimated parameters that express the geometric anisotropy in a spatial model (greater continuity angle and anisotropy factor), in relation to its influence on the spatial estimation.…”

Section: Introductionmentioning

confidence: 99%

Influence of incorporating geometric anisotropy on the construction of thematic maps of simulated data and chemical attributes of soi

Guedes

Uribe-Opazo

Ribeiro

2013

Chilean J. Agric. Res.

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The study on spatial variability of soil properties performed through geostatistical techniques allow us to identify the spatial distribution of phenomena by means of a spatial model that considers degree of dependence among observed data, depending on distance and also the direction that separate them, if there is geometric anisotropy, in other words, a directional trend in spatial continuity. However, the main difficulty in decision making regarding the use of anisotropic spatial model focuses on its relevance to the parameters that express the geometric anisotropy in a spatial model exercise in relation to the estimation space. This study aims at identifying the degree of influence of geometric anisotropy on the accuracy of spatial estimation using simulated data sets with different sample sizes and soil chemical properties such as: Fe, potential acidity (H + Al), organic matter and Mn. Comparing the isotropic and anisotropic models, especially for smaller sample sizes (100 and 169) showed an increased sum of squares of differences between predictions anisotropy factor (Fa) equals 2. Furthermore, from Fa equals 2.5, over 50% of the simulations showed values of overall accuracy (OA) of less than 0.80 and values for the concordance index Kappa (K) and Tau (T) from 0.67 to 0.80, indicating differences between thematic maps. Similar conclusions were obtained for chemical properties of the soil, from Fa equals 2, showing that there are relevant differences regarding the inclusion or not of geometric anisotropy.

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Section: Introductionmentioning

confidence: 99%

Influence of incorporating geometric anisotropy on the construction of thematic maps of simulated data and chemical attributes of soi

Guedes

Uribe-Opazo

Ribeiro

2013

Chilean J. Agric. Res.

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“…Since then, a few studies have shown the process systematically to transform Cartesian coordinates into stratigraphic coordinates in a real case study; among them we find a real case of sonic wave slowness in Koppe et al, (2006). Other alternatives to the unfolding techniques can be considered such as geostatistics with locally varying Anisotropy (Boisvert et al, 2009). Deutsch (2002) suggests some approximations that can be made to transform Cartesian coordinates into stratigraphic coordinates.…”

Section: Methodsmentioning

confidence: 99%

How the use of stratigraphic coordinates improves grade estimation

Rubio

Koppe

Costa

et al. 2015

Rem: Rev. Esc. Minas

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Some mineral deposits show mineralization along layers. These layers may pass through several subsequent geological events such as folding and/or severe erosional processes. Grades within these deposits tend to be correlated along orientations where the mineralization was originally deposited or along the same geological period (stratigraphic level). Consequently, some locations close to each other in terms of geographical coordinates can show uncorrelated grades. Spatial continuity analysis can also be affected by error inflicted by combining samples from different stratigraphic levels. This article uses the coordinate transformation (unfolding) to align the grades measured along the same stratigraphic level. The modification in coordinates improved the spatial continuity modeling and the grade estimates at non-sampled locations. The results showed that the mean of the relative error between the estimated value and the real value of the samples using unfolding is -0.10%. However, when using the original coordinates, the mean of the relative error is -0.65%. Furthermore, the correlation between the real and estimated value using crossvalidation is greater using stratigraphic coordinates. A complete case study in a manganese deposit illustrates the methodology.

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“…Geostatistical interpolation methods considering the local anisotropy (e.g. Boisvert et al, 2009;Gyasi-Agyei, 2016) could also be extended to perform local stochastic simulation.…”

Section: Contribution Of This Studymentioning

confidence: 99%

A non-stationary stochastic ensemble generator for radar rainfall fields based on the short-space Fourier transform

Nerini

Bešič

Sideris

et al. 2017

Hydrol. Earth Syst. Sci.

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Abstract. In this paper we present a non-stationary stochastic generator for radar rainfall fields based on the short-space Fourier transform (SSFT). The statistical properties of rainfall fields often exhibit significant spatial heterogeneity due to variability in the involved physical processes and influence of orographic forcing. The traditional approach to simulate stochastic rainfall fields based on the Fourier filtering of white noise is only able to reproduce the global power spectrum and spatial autocorrelation of the precipitation fields. Conceptually similar to wavelet analysis, the SSFT is a simple and effective extension of the Fourier transform developed for space-frequency localisation, which allows for using windows to better capture the local statistical structure of rainfall. The SSFT is used to generate stochastic noise and precipitation fields that replicate the local spatial correlation structure, i.e. anisotropy and correlation range, of the observed radar rainfall fields. The potential of the stochastic generator is demonstrated using four precipitation cases observed by the fourth generation of Swiss weather radars that display significant non-stationarity due to the coexistence of stratiform and convective precipitation, differential rotation of the weather system and locally varying anisotropy. The generator is verified in its ability to reproduce both the global and the local Fourier power spectra of the precipitation field. The SSFT-based stochastic generator can be applied and extended to improve the probabilistic nowcasting of precipitation, design storm simulation, stochastic numerical weather prediction (NWP) downscaling, and also for other geophysical applications involving the simulation of complex nonstationary fields.

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Kriging in the Presence of Locally Varying Anisotropy Using Non-Euclidean Distances

Cited by 65 publications

References 13 publications

Influence of incorporating geometric anisotropy on the construction of thematic maps of simulated data and chemical attributes of soi

Influence of incorporating geometric anisotropy on the construction of thematic maps of simulated data and chemical attributes of soi

How the use of stratigraphic coordinates improves grade estimation

A non-stationary stochastic ensemble generator for radar rainfall fields based on the short-space Fourier transform

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