The Digital Twin of the Coast (DTC) is a groundbreaking concept that uses interactive simulations to improve decision-making and promote sustainability in coastal science. DTC effectively combines observations, artificial intelligence, advanced modeling, and high-performance computing to unite digital replicas, forecasting, and what-if scenario simulations of the coastal systems. However, there are several challenges to overcome in achieving DTC's objectives, including the integration of heterogeneous data with multiple coordinate systems, multidimensional data analysis, feature extraction, high-fidelity scene modeling, and interactive virtual-real feedback. Here, we proposed a new mathematical foundations, the geometric algebra as well as the related data processing methods, the hypercomplex signal processings to offer promising solutions to these challenges. This study focus on the key component, the information model of DTC. We investigate a range of techniques, including geometric algebra, Clifford signal processing, and hypercomplex machine learning, as the theoretical foundation for information model of DTC. We also developed various key components of the DTC, such as data representation and information fusion, feature extraction and pattern recognition, intelligent process simulation and forecasting, as well as visualization and interactive virtual-real feedback. Our research demonstrates that geometric algebra and hypercomplex signal processing provide innovative solutions for DTC advancement and resolving scientific challenges in oceanography and broader earth science.

Digital twins,Mathematical model,Artificial Intelligence,coastal zone