NASA's Earth Science Division (ESD) conducts a wide range of satellite and suborbital missions to observe Earth's land surface and interior, biosphere, atmosphere, cryosphere, and oceans as part of a program to improve understanding of Earth as an integrated system. Earth observations provide the foundation for critical scientific advances and environmental data products derived from these observations are used in resource management and for an extraordinary range of societal applications including weather forecasts, climate projections, sea level change, water management, disease early warning, agricultural production, and the response to natural disasters. As the complexity of societal infrastructure and its vulnerability to environmental disruption increases, the demands for deeper scientific insights and more actionable information continue to rise. To serve these demands, NASA's ESD is challenged with optimizing the partitioning of its finite resources among measurements intended for exploring new science frontiers, carefully characterizing long-term changes in the Earth system, and supporting ongoing societal applications. This challenge is most acute in the decisions the Division makes between supporting measurement continuity of data streams that are critical components of Earth science research programs and the development of new measurement capabilities. This report seeks to establish a more quantitative understanding of the need for measurement continuity and the consequences of measurement gaps. Continuity of NASA's Earth's Observations presents a framework to assist NASA's ESD in their determinations of when a measurement or dataset should be collected for durations longer than the typical lifetimes of single satellite missions.