Stochastic simulation of large grids using free and public domain software
This paper proposes a tiled map procedure enabling sequential indicator simulation on grids consisting of several tens of millions of cells, without putting excessive memory requirements. Spatial continuity across map tiles is handled by conditioning adjacent tiles on their shared boundaries. Tiles across the area can be characterized by dissimilar models of spatial continuity (semi-variograms) thus relieving the requirement of a global stationarity decision. Additionally, the approach provides a simple mechanism for reseeding the pseudo random number generator. Implementation of the algorithm involved small modifications to a GSLIB program and Bash and awk scripting. The software was stable on several platforms, including 32-bit systems with a 4 Gb memory addressing limit. In an experiment we simulated 25 realizations of a 11,274 x 13,000 grid representing local uncertainty in the Dutch land cover at 25 m resolution. With the objective of mimicking the typical absence of well-distributed hard reference data, the simulations were only conditioned on local prior class probabilities and semi-variograms. Output was evaluated on the basis of reproduction of target levels of (1) cover type proportions, (2) overall class label accuracy and (3) spatially averaged local Shannon entropy. As expected, the realized statistics differed significantly from the target levels. However, the differences were consistent over the borders and the insides of map tiles. Thus, they did not result from the tiled map procedure but rather should be attributed to the used semi-conditional sequential indicator simulator. The current implementation can easily be adapted to accept other simulation algorithms. (C) 2005 Elsevier Ltd. All rights reserved.
sequential indicator simulation gslib geostatistics bash script quadtree