ON MODEL COMPLEXITY AND DATA NEEDS: TRANSIENT STORAGE AND NUTRIENT SPIRALING IN STREAMS

Streams and rivers are inherently complex systems in which a suite of physical, chemical, and biological processes determine solute fate. In response to this complexity, mathematical models have been developed in an attempt to separate and quantify individual processes. Proper application of these models is dependent on suitable data sets that contain sufficient information to quantify the effects of individual processes. Model development and application thus requires a level of complexity that is commensurate with available data. At one extreme, overly complex models are of little use if available data sets do not contain enough information for proper calibration (parameter estimation). At the other extreme, implementation of overly simple models may result in a lumped representation of system behavior that does little to elucidate the effects of individual processes. These two extremes are illustrated using two contemporary concepts in stream ecology: transient storage and nutrient spiraling. For the case of transient storage, a relatively simple modeling approach is used in which the processes of surface storage and hyporheic exchange are lumped into a single storage term (e.g., as in OTIS). This conceptual model is known to be in error as surface storage and hyporheic exchange may occur at vastly different time scales, such that the single storage term is a lumped composite representing average conditions. As such, more complex models of transient storage have been proposed in which multiple storage zones are formulated. This increase in model complexity has not been matched by advances in data collection methods that allow for calibration of the parameters introduced by the additional storage zones. Application of multiple storage zone models may therefore not be warranted as parameter estimates may be highly subjective. For the case of nutrient spiraling, uptake lengths are estimated using a simple model in conjunction with steady-state nutrient data. Model application results in parameter estimates that lump the effects of main channel and storage-zone uptake. In contrast to the case of transient storage, data collection methods that provide additional process information (i.e. the collection of time-series data) are readily available, such that the use of a more complex model is warranted.