A Change of Support Model Optimization for Environmental Monitoring

Geometric representations of spatial domains in environmental applications are used to structure, access and render surveyed data; the survey domain is often represented as a discrete regular grid with a fixed spatial resolution, because of its conceptual and implementation simplicity. Nevertheless, the region of interest (ROI) can be delimited by physically-defined criteria leading to boundaries with complex geometries. Such constraints force a representation of free-form domains by means of regular grids with very high-resolution models made of millions or even billions of small elements, requiring high-performance computers to be handled efficiently. Unstructured grids are more suitable to represent free-form domains and flexible to faithfully represent complex geometries. Moreover, samples used to fill the ROI with interpolation algorithms are often collected with a point support, z(ui ), i = 1, ... , N, while the estimates are instead required over volumes, Z(vk ), k = 1, ... , Nb . Change-ofsupport techniques for additive variables have been previously published in the literature to fill the gap and make unstructured grids suitable for environmental modelling (Chiles and Delfiner, 2009). Among the existing change-of-support techniques, the Discrete Gaussian Model (DGM) is one of the most used techniques for environmental applications where the discrete units are represented by irregular shapes. Traditional approach of DGM define a coefficient, r, as the correlation between a point value and a volumetric one, so that we can switch from one support to another, without a bias. This coefficient is related to the blockto- block covariance and therefore in a multi-support context of volumes this coefficient will be different from one volume to another, rk , k = 1, ... , Nb. The greater the size of a volume vk the smaller the coefficient rk (it will tend to zero); on the other hand, when the volume will tend to the point size, the coefficient will tend to one (maximum correlation). The use of different discretization schemes of quasi-random points for the calculation of block-to-block covariance can affect the results. We implemented an extension of Sobol' sequences to 3D unstructured problems to compute the change-of-support coefficients more efficiently. We implement the aforementioned theoretical aspects in a specific code applied to a simulation framework that corresponds to an adaptive real-time environmental monitoring for the evaluation of geochemistry in marine waters. We represent the harbor water body by an unstructured grid to describe the highly irregular geometry at finer level: smaller grid cells are generated near the coast to better capture the complex geometries of the seashore; larger ones elsewhere. The first results demonstrate that taking into account the support dependency, enables the optimization in terms of accuracy and computational cost the analysis when the support of available data is different by the supports of the unstructured grid for which statements are required for the estimation. Subsequently, this method will be validated on the harbor waters model.