Alternative reference frames in river system science

Understanding environmental processes begins with basic mental conceptualizations of system components and interactions.  In understanding rivers, two conceptualizations are the basis for observing movement: Eulerian, where object fluxes are observed in a spatially bounded area, or Lagrangian, where specific objects are tracked through time.  Mechanistic studies include Eulerian and Lagrangian data, with the challenge being to negotiate how much Eulerian and Lagrangian information is needed to maximize accuracy of understanding processes and data collection efficiency. 
In nutrient spiraling, like most river research, the research reference frame is presupposed.  However, we believe that conceptual breakthroughs in river system science lurk in explicit alterations of presupposed reference frames.  By adopting alternative or non-intuitive approaches, novel questions and observations are more likely.  We develop an example by re-conceptualizing and analyzing nutrient “movement” in ecosystems.  Starting with Eulerian-based nutrient budgets, we used a stochastic modeling approach to invert Eulerian data into a semi-Lagrangian representation of nutrient movement through a stream foodweb.  This representation emphasizes the importance of trophic interactions rather than advection on nutrient dynamics in streams. 
Re-thinking our mental constructions of river systems is not new theory, but may be useful for developing new theory and insights.