The world is dynamic, so are big data. The evolving challenges of managing big data volume, variety, veracity, validity, and velocity has resulted in several studies focusing on solving one or more of these perplexing issues. In this Ph.D. research, I focus on the evolving issues arising from big data variety, veracity, privacy, and accessibility. First, I design a conceptual model for capturing and storing variety of big data types including structured, semi-structured and unstructured data types and in addition, design a metadata collection framework for managing the big data in support of machine learning and open data FAIR principle of Findable, Accessibility, Interoperability and Re-usability such that the information about the data are available beyond the life cycle of the data. Second, I design hierarchical spatial-temporal model (HSTM) for managing individual record in big data in the aforementioned open data lake architecture with metadata collection framework. Third, I extend the HSTM and design the resulting hierarchical spatial-temporal privacy preserving model (HSTPPM) for preserving privacy of individual record in big data. Fourth, I extend and design applications of the HSTPPM to big data co-occurrence pattern mining and big data visualization.