Quantitatively directed sampling for main channel and hyporheic zone water-quality modeling

Management of water quality in streams and rivers, including determinations and allocations of acceptable total maximum daily loads (TMDLs), requires use of calibrated and reliable water quality models for prediction of pollutant concentrations under alternative management or load allocation scenarios. However, the accuracy and reliability (precision) of a model can be no greater than those of the input parameters upon which its predictions are based. Thus, questions facing model users concern which of the potentially many model parameters should be estimated based on field sampling, and where those parameters should be sampled along the length of a stream. Quantitatively directed exploration (QDE), a quantitative method for directing field sampling efforts, is presented herein as a mean to both identify parameters to sample, and where to sample them. The QDE approach is demonstrated for a stream where the transient storage effects of the hyporheic zone are important considerations for water quality modeling. The fundamental idea underlying QDE is that the reliability (i.e. variance) of a model-predicted result is a function of the variances of the model inputs. By examining individual contributions to the total variances of model predictions, it provides a means for identification of those parameters and their sampling locations that have the greatest influences. In doing so, it yields an objective and quantifiable way to reduce the model output variance, and hence to improve the reliability of the model results. In this paper, model predictions are taken as pollutant concentrations in a stream channel. In the interest of making a clear exposition of the QDE approach, while not cluttering the presentation with unnecessary complications, the water quality model used in this paper is a simple feed-forward system of continuously stirred tank reactors (CSTRs).