Time and length scales for the one‐dimensional assumption and its relation to ecological models

Abstract

The vertical one‐dimensional assumption is examined with respect to its validity for mathematical ecological models of lakes or reservoirs. Analysis of the time and length scales characterizing the hydrodynamics, chemistry, and biology shows that the two scales are inexorably coupled and their interaction dictates both upper and lower bounds for the lake size that can be characterized by a one‐dimensional model. For an update frequency or forcing time scale of 1 day the one‐dimensional model is restricted to lakes characterized by length scales of 0.5–10 km. This range is preliminary and dependent on model formulation and update frequency. Inconsistencies between the model formulation scales for the hydrodynamics, chemistry, and biology may result in erroneous model predictions.