Multifidelity methods for data fusion of environmental data

Multifidelity models are a type of data fusion approach that use information from multiple data sources arranged in a hierarchy. This structure is especially useful in environmental modelling, where data sources naturally differ in terms of reliability, resolution, and how often they are available. Although Gaussian processes—the foundation of multifidelity models—are commonly used in environmental science, their application in multifidelity settings has been quite limited. This thesis explores the use of multifidelity modeling for combining environmental data from different sources, with a focus on wind speed as a representative example. It examines when multifidelity methods are useful and compares them with standard methods used in the industry. As part of this work, the multifidelity model is extended to handle skewed data by introducing a new method called the Warped Multifidelity Gaussian Process (WMFGP). In addition, a scalable framework for modeling both spatial and temporal data is developed. This framework leveraged the use of Vecchia approximation to make complex multifidelity models more efficient. Both the WMFGP and the scalable framework prove effective in modeling wind speed data from Lombardy, a region in northern Italy.