Adaptive environmental sampling: The interplay between geostatistics and geometry

In environmental surveys a large sampling effort is required to produce accurate geostatistical maps representing the distribution of environmental variables, and the analysis of each sample is often expensive. Typically, the sample locations are completely specified in the survey design phase, prior to data-collection. Usually, the sampling points are located on a regular grid, or along directions that are selected with respect to any a-priori knowledge of the expert. No feedback is available during the survey. In this paper, we present a different sampling strategy, namely adaptive sampling. Our approach exploits geostatistics constructs in order to determine on-the fly the next best sample location. After initializing the system with few sampling points, an iterative routine predicts the variable distribution from the data sampled so far, and suggests the next sample to be acquired in order to optimize the uncertainty of the estimates. At every iteration a new sample is acquired, and the variable distribution map is refined, along with the uncertainty map related to that distribution. Our method allows to build a representation of the survey area as precise as the one provided by the traditional methods, but with less samples, thus reducing both time and costs of the survey. We show a preliminary evaluation of the adaptive strategy in the bi-dimensional case based on a synthetic scenario, and describe the generalization of these encouraging results to the full 3D domain in the concrete setting of water quality monitoring. A proper geometric representation of the three dimensional survey area, coupled with a proper visualization of distribution and related uncertainty, will provide real-time feedback during the survey.