Adaptive ensemble spatial analysis

Spatial interpolation is a frequent issue in geosciences, where the estimation of values of a variable of interest at unsampled locations is sought from some spatial samples. The techniques most frequently employed to address this issue, such as those considered in geostatistics, require an effort of modelling and characterisation of statistics. This has limited a greater use of these techniques in disciplines that work with spatial or spatio-temporal information. This paper presents a novel spatial analysis technique, which is an extension of a previously proposed ensemble spatial interpolation model. It aims to provide a methodology that is as data-driven as possible, useful for a more general geoscientific (or expert) audience, and capable of providing quality estimates without the need for specific classical geostatistical expertise, such as variographic analysis. Additionally, a reinterpretation of the ensemble spatial interpolation algorithm is presented as a generative Bayesian model, which offers a simple and insightful reinterpretation of the concept of spatial interpolation in general. Finally, an extensive series of experiments, using both real and synthetic data, is presented to test the limits of the proposed model in very demanding scenarios, comparing it with a traditional geostatistical model. The results obtained verify a good performance in the ability to capture the relevant spatial aspects, even in challenging conditions such as non-stationary cases or when there are few samples to perform the inference. In turn, the level of errors in validation contexts is similar to those obtained with traditional geostatistics (Ordinary Kriging method), in synthetic contexts that are suitable for the use of geostatistical techniques. In future work, further research can be considered to improve local spatial characterisation, as well as to use the proposed technique in spatial 3D case studies.