Geostatistical modelling of spatial uncertainty using p -field simulation with conditional probability fields

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Abstract
This paper presents a variant of p-field simulation that allows generation of spatial realizations through sampling of a set of conditional probability distribution functions (ccdf) by sets of probability values, called p-fields. Whereas in the common implementation of the algorithm the p-fields are nonconditional realizations of random functions with uniform marginal distributions, they are here conditional to 0.5 probability values at data locations, which entails a preferential sampling of the central part of the ccdf around these locations. The approach is illustrated using a randomly sampled (200 observations of the NIR channel) SPOT scene of a semi-deciduous tropical forest. Results indicate that the use of conditional probability fields improves the reproduction of statistics such as histogram and semivariogram, while yielding more accurate predictions of reflectance values than the common p-field implementation or the more CPU-intensive sequential indicator simulation. Pixel values are then classified as forest or savannah depending on whether the simulated reflectance value exceeds a given threshold value. In this case study, the proposed approach leads to a more precise and accurate prediction of the size of contiguous areas covered by savannah than the two other simulation algorithms.