Geostatistical Applications of Spartan Spatial Random Fields

Elogne, S.N.; Hristopulos, Dionissios T.

doi:10.1007/978-1-4020-6448-7_39

Cited by 9 publications

(10 citation statements)

References 5 publications

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“…Consideration of various parametric covariance models may not be necessary in the SSRF framework, since the four-parameter SSRF covariance function is sufficiently flexible to capture different spatial patterns (Hristopulos 2003;Elogne and Hristopulos 2006c) within a statistically homogeneous domain. An automatic mapping system should test the assumption of statistical homogeneity.…”

Section: Discussionmentioning

confidence: 99%

“…Extensions of these formulas for irregular sampling networks using kernel functions are given in Elogne and Hristopulos (2006a). After the Spartan parameters are estimated, spatial interpolation of the field at unobserved locations can be accomplished by means of the following procedures: (1) using classical kriging methods in conjunction with the corresponding Spartan dependence structure, e.g., (Elogne and Hristopulos 2006c); (2) using the idea of local low energy estimators (Hristopulos 2006) or (3) by means of the SSRF mode predictor (Hristopulos and Elogne 2006b). The first method only differs from the classical approach in the covariance function used.…”

Section: The Ssrf Model Of Spatial Dependencementioning

confidence: 99%

“…In most cases that we have investigated this is sufficient to obtain convergence of the algorithm to a solution that appears to be unique (although we do not have a rigorous proof of this statement). Only in one case study different initial values of g 1 (0) led to different covariance structures (Elogne and Hristopulos 2006c). The initial value n (0) of the characteristic length is estimated from the data.…”

Section: Spartan Parameter Inferencementioning

confidence: 99%

See 2 more Smart Citations

An application of Spartan spatial random fields in environmental mapping: focus on automatic mapping capabilities

Elogne

Hristopulos

Varouchakis

2007

Stoch Environ Res Risk Assess

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This paper investigates the potential of Spartan spatial random fields (SSRFs) in real-time mapping applications. The data set that we study focuses on the distribution of daily gamma dose rates over part of Germany. Our goal is to determine a Spartan spatial model from the data, and then use it to generate ''predictive'' maps of the radioactivity. In the SSRF framework, the spatial dependence is determined from sample functions that focus on short-range correlations. A recently formulated SSRF predictor is used to derive isolevel contour maps of the dose rates. The SSRF predictor is explicit. Moreover, the adjustments that it requires by the user are reduced compared to classical geostatistical methods. These features present clear advantages for an automatic mapping system. The performance of the SSRF predictor is evaluated by means of various cross-validation measures. The values of the performance measures are similar to those obtained by classical geostatistical methods. Application of the SSRF method to data that simulate a radioactivity release scenario is also discussed. Hot spots are detected and removed using a heuristic method. The extreme values that appear in the path of the simulated plume are not captured by the currently used Spartan spatial model. Modeling of the processes leading to extreme values can enhance the predictive capabilities of the spatial model, by incorporating physical information.

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Section: Discussionmentioning

confidence: 99%

Section: The Ssrf Model Of Spatial Dependencementioning

confidence: 99%

Section: Spartan Parameter Inferencementioning

confidence: 99%

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An application of Spartan spatial random fields in environmental mapping: focus on automatic mapping capabilities

Elogne

Hristopulos

Varouchakis

2007

Stoch Environ Res Risk Assess

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“…Hence, in its current formulation DGC is more useful for smooth data distributions, such as the ones studied herein. For noisy data, improvements can be made by developing directional kernel-based estimators for the square gradient and curvature in the spirit of (Elogne & Hristopulos, 2008;Hristopulos & Elogne, 2009) or by incorporating an initial filtering stage to reduce noise (Brownrigg, 1984;Yin, 1996). DGC does not rely on assumptions about the probability distribution of the data, it is reasonably efficient computationally, and it requires very little user input (i.e., the number of simulation runs, the number of class levels and the size of the maximum stencil for initial state selection).…”

Section: Discussionmentioning

confidence: 99%

A Directional Gradient-Curvature method for gap filling of gridded environmental spatial data with potentially anisotropic correlations

Žukovič¹,

Hristopulos²

2013

Atmospheric Environment

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We introduce the Directional Gradient-Curvature (DGC) method, a novel approach for filling gaps in gridded environmental data. DGC is based on an objective function that measures the distance between the directionally segregated normalized squared gradient and curvature energies of the sample and entire domain data. DGC employs data-conditioned simulations, which sample the local minima configuration space of the objective function instead of the full conditional probability density function. Anisotropy and non-stationarity can be captured by the local constraints and the directiondependent global constraints. DGC is computationally efficient and requires minimal user input, making it suitable for automated processing of large (e.g., remotely sensed) spatial data sets. Various effects are investigated on * Corresponding author.Email addresses: milan.zukovic@upjs.sk (MilanŽukovič), dionisi@mred.tuc.gr (Dionissios T. Hristopulos) URL: http://www.mred.tuc.gr/home/hristopoulos/dionisi.htm (Dionissios T. Hristopulos) Preprint submitted to Atmospheric EnvironmentJuly 3, 2018 synthetic data. The gap-filling performance of DGC is assessed in comparison with established classification and interpolation methods using synthetic and real satellite data, including a skewed distribution of daily column ozone values. It is shown that DGC is competitive in terms of cross validation performance.

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“…In this section we obtain space-time covariances from the equation that governs the motion of the STRF realizations. Based on (11) and (26)…”

Section: Covariance Function From Langevin Equationmentioning

confidence: 99%

Space-time models based on random fields with local interactions

Hristopulos

Tsantili

2016

Int. J. Mod. Phys. B

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The analysis of space-time data from complex, real-life phenomena requires the use of flexible and physically motivated covariance functions. In most cases, it is not possible to explicitly solve the equations of motion for the fields or the respective covariance functions. In the statistical literature, covariance functions are often based on mathematical constructions. We propose deriving space-time covariance functions by solving "effective equations of motion", which can be used as statistical representations of systems with diffusive behavior. In particular, we propose using the linear response theory to formulate space-time covariance functions based on an equilibrium effective Hamiltonian. The effective space-time dynamics are then generated by a stochastic perturbation around the equilibrium point of the classical field Hamiltonian leading to an associated Langevin equation. We employ a Hamiltonian which extends the classical Gaussian field theory by including a curvature term and leads to a diffusive Langevin equation. Finally, we derive new forms of space-time covariance functions.

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Geostatistical Applications of Spartan Spatial Random Fields

Cited by 9 publications

References 5 publications

An application of Spartan spatial random fields in environmental mapping: focus on automatic mapping capabilities

An application of Spartan spatial random fields in environmental mapping: focus on automatic mapping capabilities

A Directional Gradient-Curvature method for gap filling of gridded environmental spatial data with potentially anisotropic correlations

Space-time models based on random fields with local interactions

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