A Real-Time Adaptive Sampling Strategy Optimized by Uncertainty for Spatial Data Analysis on Complex Domains

Environmental monitoring is used to reveal the state of the environment, to inform experts and help them to prioritise actions in the context of environmental policies. Environmental sampling is the way the environment is interrogated to get measures of environmental (e.g., physical, chemical) parameters in a limited set of locations (samples). The environmental properties varies from place to place in continuum and there are infinitely many places at which we might record what they are like, but practically we can measure them at only a finite number by sampling. The role of the location in which samples are collected is very crucial. The focus of the thesis is the study of a mathematical framework that supports a reasoned and non-random sampling of environmental variables, with the aim of defining a methodological approach to optimise the number of sampling required while maintaining a target precision. The arrangement of points is not selected or known a priori; conversely, we propose an iterative process where the next-sample location is determined on-the-fly on the basis of the environmental scenario that is delineated more and more accurately at each iteration. At each iteration, the distribution map is updated with the new incoming data. The geostatistical analysis we implement provides a predicted value and the related uncertainty about that value, actually providing an uncertainty map beside the predicted distribution. The system responds to the current state by requiring a measurement in the area with highest uncertainty, to reduce uncertainty and increase accuracy. Environmental survey areas to monitor are often characterised by very complex boundaries. Unstructured grids are more flexible to faithfully represent complex geometries compared to structured grids. The usage of unstructured grids introduces another innovation aspect studied in the thesis, which is the change of support model.