Nitrogen loss rates in streams: Scale-dependence and up-scaling methodology

We show that the large spatial aggregation of model parameters in common catchment scale nitrogen budget modeling leads to artifacts that may, for instance, be a factor in explaining reported decreases of calibrated instream nitrogen loss rates, lambda(s)(*), with increasing stream size. In general, the common assumption of a single representative solute travel time for an entire stream reach may lead to considerable underestimation of the actual underlying local biogeochemical loss rate lambda(s) by lambda(s)(*), which increases with actual lambda(s) value and/ or increasing mean solute travel time and travel time variability in the stream. We propose an up-scaling methodology to overcome such model artifacts, in form of closed-form expressions of catchment-scale, in-stream nitrogen delivery factors for diffuse and point sources, as functions of local-scale nitrogen loss rates, lambda(s).