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The digital twin of the ocean (DTO) is a groundbreaking concept that uses interactive simulations to improve decision-making and promote sustainability in earth science. The DTO effectively combines ocean observations, artificial intelligence (AI), advanced modeling, and high-performance computing to unite digital replicas, forecasting, and what-if scenario simulations of the ocean systems. However, there are several challenges to overcome in achieving the DTO’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. Hypercomplex signal processing offers a promising solution to these challenges, and this study provides a comprehensive overview of its application in DTO development. We investigate a range of techniques, including geometric algebra, quaternion signal processing, Clifford signal processing, and hypercomplex machine learning, as the theoretical foundation for hypercomplex signal processing in the DTO. We also review the various application aspects of the DTO that can benefit from hypercomplex signal processing, such as data representation and information fusion, feature extraction and pattern recognition, and intelligent process simulation and forecasting, as well as visualization and interactive virtual–real feedback. Our research demonstrates that hypercomplex signal processing provides innovative solutions for DTO advancement and resolving scientific challenges in oceanography and broader earth science.

Cactus is an open source problem solving environment designed for scientists and engineers. Its modular structure facilitates parallel computation across different architectures and collaborative code development between different groups. The Cactus Code originated in the academic research community, where it has been developed and used over many years by a large international collaboration of physicists and computational scientists. We discuss here how the intensive computing requirements of physics applications now using the Cactus Code encourage the use of distributed and metacomputing, and detail how its design makes it an ideal application test-bed for Grid computing. We describe the development of tools, and the experiments which have already been performed in a Grid environment with Cactus, including distributed simulations, remote monitoring and steering, and data handling and visualization. Finally, we discuss how Grid portals, such as those already developed for Cactus, will open the door to global computing resources for scientific users.