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Spatial Prediction Using Uncertain Variogram

TitleSpatial Prediction Using Uncertain Variogram
Publication TypeConference Paper
Year of Publication2014
AuthorsCaha J, Marek L, Pászto V
Conference NameDailyMeteo.org/2014
Date Published06/2014
PublisherFaculty of Civil Engineering, University of Belgrade
Conference LocationBelgrade
Abstract

Uncertainty of results is often as important as results themselves for any type of prediction. This is especially true for methods of prediction that contain epistemic uncertainty, which often takes the form of specification of parameters for the prediction method. These parameters are usually determined by an expert knowledge and perceived as granted, however, their selection is often a matter of opinion and several different solutions are possible. Each of such solutions can provide different prediction. Fuzzy prediction models can be used to handle epistemic uncertainty in models and they provide results in the form of uncertain prediction, which can be used to obtain most likely prediction along with minimal and maximal values of prediction. We decided to apply and test the usability of the fuzzy prediction model, which was developed and described by Loquin and Dubois in Kriging with Ill-Known Variogram and Data (2010). In this article we study the influence of epistemic uncertainty of variogram parameters (sill, range, and nugget) selection on results of spatial interpolation of two datasets. Particularly, the well-known and well described meuse data set is used as one of data sources, while the second data set is the collection of mean atmospheric pollution measurements (PM10) in the Czech Republic in 2013. Three possible variograms are selected for each dataset. Modal variogram is constructed as the most likely optimal variogram, while minimal and maximal variograms provide bounds for possible realizations of variograms. The fuzzy surface construction is based on optimisation scheme given by Loquin and Dubois (2010) [8]. The fuzzy surface is than compared against surfaces with simulated parameters from the range specified by minimal and maximal variograms in order to determine its usefulness as boundaries of uncertainty caused by user’s selection of variogram parameters. These predictions are further studied. Although the validity of the presented optimisation scheme is not fully proved, the usability and analysis of errors still show only up to 6% of acceptable errors out of 5 000 simulations. That proves the suitability of the procedure for the spatial prediction based on kriging with uncertain variogram.

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