We illustrate the use of our partial differential equations and super-accurate composition schemes for flow maps to quantify Lagrangian transports and non-advective dynamics in geophysical fluid flows. Flow maps are spatiotemporal fields governed by PDEs that correspond to an infinite number of classic trajectories governed by ODEs (the characteristics of the PDEs). We utilize our flow map predictions to extract dynamical regions and coherent structures, classify ocean processes, and inform classical geophysical fluid dynamics analyses. Our emphasis is on the use of spatiotemporal flow maps to help differentiate the advective transports from non-advective transformations of water masses and ocean features in four dimensions. Results are presented for real-time sea experiments with autonomous sensing platforms and advanced modeling systems in diverse ocean regions and dynamical regimes. They include the Nova Scotia Shelf-Slope and New England Seamount Chain regions, the Gulf of Mexico, and the Balearic and Alboran Seas in the western Mediterranean. Our differentiations directly highlight regions of higher shear and mixing, including the submesoscale features, the edges of meanders, eddies, filaments, and internal waves, and the regions undergoing strong vertical and helical-spiral motions.