Rivers convey a broad range of materials, such as sediment, nutrients, and contaminants. Much of this transport can occur during or immediately after an episodic, pulsed event like a flood or an oil spill. Understanding the flow processes that influence the motion of these substances is important for managing water resources and conserving aquatic ecosystems. This study introduces a new remote sensing framework for characterizing dynamic phenomena at the scale of a channel cross-section: Hyperspectral Image Transects during Transient Events in Rivers (HITTER). We present a workflow that uses repeated hyperspectral scan lines acquired from a hovering uncrewed aircraft system (UAS) to quantify how a water attribute of interest varies laterally across the river and evolves over time. Data from a tracer experiment on the Missouri River are used to illustrate the components of the end-to-end processing chain we used to quantify the passage of a visible dye. The framework is intended to be flexible and could be applied in a number of different contexts. The results of this initial proof-of-concept investigation suggest that HITTER could potentially provide insight regarding the dispersion of a range of materials in rivers, which would facilitate ecological and geomorphic studies and help inform management.