Optimal incorporation of massive satellite and ground-based data sets into physical models of the earth's near-space environment has received significant attention in recent years due to the increasing demands for space weather specification and prediction. Assimilative models developed to investigate ionospheric, magnetospheric, and solar phenomena face challenges imposed by modeling accuracy, statistical characterization, and computational requirements. Meteorological and oceanographic communities have encountered similar problems in modeling complex hydrodynamical systems and uncertainties caused by incomplete understanding of numerous interactions and technological limits on the attainable spatial/temporal resolution. In general, the optimality of the assimilation technique is either approached on statistical grounds through recursive estimation and optimal filtering strategies or based on deterministic vector optimization techniques. The work described here demonstrates the relationship between these approaches by establishing the statistical interpretation of variational techniques in inverse imaging and, more importantly, the impact on the design of appropriate cost functions for the data assimilation task at hand. One example is a data-assimilative model of the solar corona incorporating UV cronograph observations aimed to investigate the role of the anisotropic ion velocity distributions in energizing the solar wind. Another example is a global model of the earth's ionosphere ingesting UV brightness data to investigate a range of ionospheric processes. Open questions regarding model order selection and the determination of optimal data-supported model resolution for a given observing scenario are also discussed and some directions toward their efficient implementation are explored. Such analytical characterization of model behavior can be used in optimal experiment design involving configuration of a multi-sensor observation system.