Abstract
Automatically generating maps of a measured variable of interest can be problematic. In this work we focus on the monitoring network context where observations are collected and reported by a network of sensors, and are then transformed into interpolated maps for use in decision making. Using traditional geostatistical methods, estimating the covariance structure of data collected in an emergency situation can be difficult. Variogram determination, whether by method-of-moment estimators or by maximum likelihood, is very sensitive to extreme values. Even when a monitoring network is in a routine mode of operation, sensors can sporadically malfunction and report extreme values. If this extreme data destabilises the model, causing the covariance structure of the observed data to be incorrectly estimated, the generated maps will be of little value, and the uncertainty estimates in particular will be misleading. Marchant and Lark (2007) propose a REML estimator for the covariance, which is shown to work on small data sets with a manual selection of the damping parameter in the robust likelihood. We show how this can be extended to allow treatment of large data sets together with an automated approach to all parameter estimation. The projected process kriging framework of Ingram et al. (2008) is extended to allow the use of robust likelihood functions, including the two component Gaussian and the Huber function. We show how our algorithm is further refined to reduce the computational complexity while at the same time minimising any loss of information. To show the benefits of this method, we use data collected from radiation monitoring networks across Europe. We compare our results to those obtained from traditional kriging methodologies and include comparisons with Box–Cox transformations of the data. We discuss the issue of whether to treat or ignore extreme values, making the distinction between the robust methods which ignore outliers and transformation methods which treat them as part of the (transformed) process. Using a case study, based on an extreme radiological events over a large area, we show how radiation data collected from monitoring networks can be analysed automatically and then used to generate reliable maps to inform decision making. We show the limitations of the methods and discuss potential extensions to remedy these.
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German Federal Office for Radiation Protection.
References
Box GEP, Cox DR (1964) An analysis of transformations. J R Stat Soc 26(2):211–252
Cressie N, Hawkins DM (1980) Robust estimation of the variogram: I. Math Geol 12(2):115–125
Csató L, Opper M (2002) Sparse online Gaussian processes. Neural Comput 14(3):641–669
Diggle PJ, Tawn JA, Moyeed RA (1998) Model-based geostatistics. Appl Stat 47:299–350
Genton MG (1998) Highly robust variogram estimation. Math Geol 30(2):213–221
Ingram B, Csató L, Evans D (2005) Fast spatial interpolation using sparse Gaussian processes. Appl GIS 1(2):15:1–17
Ingram B, Cornford D, Evans D (2008) Fast algorithms for automatic mapping with space-limited covariance functions. Stoch Environ Res Risk Assess 22(5):661–670
Marchant BP, Lark RM (2007) Robust estimation of the variogram by residual maximum likelihood. Geoderma 140(1–2):62–72
Pilz J, Pluch P, Spoeck G (2004) Bayesian Kriging with lognormal data and uncertain variogram parameters. In: Proceedings of the Fifth European Conference on geostatistics for environmental applications. Springer, Berlin
Acknowledgements
This work is funded by the European Commission, under the Sixth Framework Programme, by the Contract N. 033811 with the DG INFSO, action Line IST-2005-2.5.12 ICT for Environmental Risk Management. The views expressed herein are those of the authors and are not necessarily those of the European Commission.
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Ingram, B., Cornford, D., Csató, L. (2010). Robust Automatic Mapping Algorithms in a Network Monitoring Scenario. In: Atkinson, P., Lloyd, C. (eds) geoENV VII – Geostatistics for Environmental Applications. Quantitative Geology and Geostatistics, vol 16. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-2322-3_31
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DOI: https://doi.org/10.1007/978-90-481-2322-3_31
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