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

Abstract

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.

Assessment of groundwater quality of Lakshimpur district of Bangladesh using water quality indices, geostatistical methods, and multivariate analysis

“…Among the different kriging techniques, OK has been used in this study because of its easy calculation and prediction accuracy compared to the other kriging methods (Gorai and Kumar 2013). Recently, different variograms or semivariogram models such as linear, exponential, and spherical models are very popular worldwide for spatial analysis of geochemical data sets (Kitanidis 1997;Elogne et al 2008;Varouchakis and Hristopulos 2013). In this study, circular, spherical, exponential, and Gaussian models have been used to measure spatial autocorrelation or dependence of the groundwater data.…”

Stochastic Local Interaction (SLI) model: Bridging machine learning and geostatistics

“…The SLI model extends previous research on Spartan spatial random fields [13,21,22] to an explicitly discrete formulation and thus enables its application to scattered data without the approximations used in [23]. SLI is based on a joint probability density function (pdf) determined from local interactions.…”

“…The data were provided by the German automatic radioactivity monitoring network for the Spatial Interpolation Comparison Exercise 2004 (SIC 2004) [12]. This data set is well studied and thus allows easy comparisons with other methods [13].…”

Towards generic real-time mapping algorithms for environmental monitoring and emergency detection

“…Also, approaches that reduce the need for ''off-line'' structural adaptation as proposed in the previous step add flexibility to the mapping algorithm and may better adapt to a specific dataset. One example for this direction of research is the Spartan spatial random field predictor of Elogne et al (2007). Barry and Ver Hoef (1996) presented a black-box approach to kriging in which semivariograms are chosen and fitted automatically, but a number of unresolved problems remain, the main one being the overestimation of the spatial correlation at very short distances, the so-called nugget effect.…”