Exploratory visualization and analysis of time-dependent vector fields or flow fields generated by scientific simulations is increasingly challenging on modern supercomputers. One possible solution is the use of a Lagrangian-based in situ reduction and post hoc exploration approach. Although this approach offers improved accuracy-storage propositions, prior work has failed to evaluate the viability and efficacy of this method at scale. Additionally, there is a lack of understanding surrounding best practices that advance the effectiveness of the Lagrangian-based approach. This dissertation contributes empirical studies measuring absolute error, calculating the practical in situ encumbrance, and understanding tradeoffs involving accuracy, storage, and performance. Further, this dissertation proposes algorithms that 1) improve accuracy-storage propositions via improved in situ seed placement and post hoc interpolation, and 2) achieve scalability via a communication-free model. Overall, the research presented in this dissertation establishes the viability and efficacy of using Lagrangian representations extracted in situ for post hoc exploratory visualization of large time-dependent vector fields.