Compartmental modeling approach for evaluating nutrient retention and attenuation in streams

Nonpoint source nutrient loads are a major cause of stream water quality impairments in the United States. Management of upland terrestrial nutrient inputs is ideal, but is often not feasible. Management of nutrient assimilative capacity in the stream corridors of small watersheds may be undertaken, but the linkages between specific restoration practices and assimilative capacity have yet to be well-determined. This study develops a compartmental modeling framework using concepts of systems analysis that is potentially valuable in establishing the linkage between commonly measured nutrient retention metrics and nutrient assimilative capacity.; First, transient storage in stream systems is decomposed in terms of a review of conceptual models at the physical process level relevant to small watersheds. Then, commonly used nutrient metrics are summarized.; Next, nutrient assimilative capacity is defined as the fraction of mass of a nutrient impulse that is not eluted through a stream reach. This serves as a method of diagnosis using tracer tests. Using results of a conservative tracer experiment, the transient storage component of stream flow and transport is derived as an indicial response function resulting from re-release to the free stream following a solute impulse. Parameterizations of the response are not directly related to measurable metrics, and therefore are of limited value in forward modeling of nutrient assimilative capacity. The previously introduced retention metrics are embodied in a total Damkohler number, and a process transfer function is derived that predicts nutrient assimilative capacity. A framework is developed for using this transfer function in sensitivity analysis.; Then, it is shown that the compartmental model can be used to represent the total assimilative capacity of the stream corridor of a watershed as a cascade of nutrient assimilative capacities. This approach is verified using a numerical dynamic model and results from a published field study.; Finally, application of the compartmental model is presented in a total maximum daily load (TMDL) context. A framework is developed for the margin of safety using a Bayesian model with the structural form of the transfer function guiding a noninformative prior distribution, through Monte Carlo analysis.