This paper presents a framework for constructing structure-preserving representations of complex systems through discrete approximation, and demonstrates its use in studying the vertical temperature and salinity structures in the mesopelagic zone across the global ocean using the ARGO dataset. Clustering serves as a means of organizing complexity into a finite set of structures that approximate the overall oceanic conditions, and a color encoding design then integrates these structures into a coherent map, with the three color components derived from interpretable geometric features of a profile: its initial level, its magnitude of variation, and its shape. Instead of focusing on specific depth levels or computing zonal averages within selected regions, our approach preserves the full vertical structure of individual profiles and incorporates each profile in the global ocean, capturing both fine-scale profile detail and large-scale spatial variability. By clustering over one million profiles collected over a decade, we identify and characterize representative profile shapes, which form the basis for a visualization strategy that provides an integrated, comprehensive, and interpretable presentation of the large-scale spatial distributions of these oceanic vertical patterns.

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