Estimating stream metabolism from oxygen concentrations: Effect of spatial heterogeneity

Rivers are heterogeneous at various scales. River metabolism estimators based on oxygen time series provide average estimates of net oxygen production at the scale of a river reach. These estimators are derived for homogeneous river reaches. For this reason, they cannot be used to analyze how exactly they average over longitudinal variations in net production, reaeration, oxygen saturation concentration and flow velocity. We try to fill this gap by using a general analytical solution of the transport‐reaction equation to (1) demonstrate how downstream oxygen concentration is affected by upstream concentration and (possible) longitudinally varying values of net production, reaeration, oxygen saturation concentration and flow velocity within a reach, and (2) derive how the net production estimate depends on varying upstream river parameters. In addition, we derive a new net production estimator that extends previously suggested estimators. The equations derived in this paper provide a general framework for understanding the assumptions underlying net production estimators. They are used to derive recommendations on the use of single station or two stations measurement layouts to get accurate river metabolism estimates. The estimator is implemented in the freely available statistics and graphics software package R ( www.r‐project.org ). This makes it easily applicable to observed oxygen time series. Empirical evidence of the significance of heterogeneity in rivers is demonstrated by applying the estimator to four subsequent reaches of a river using oxygen measurements from the ends of all reaches.