Empirical model for predicting a catchment-scale metric of surface water transit time in streams

Estimates of average water velocity (v(w)) extracted from tracer dye studies (v(dye)) or calculated from velocity-discharge relationships at continuous-flow gauges (v(gage)) were combined with catchment area (A) and other readily available data for 111 streams throughout the conterminous United States. The resulting data set (n = 305) represented broad ranges of A (65 - 62 419 km(2)), mainstem length (L-max, 15.6-867 km), slope (S, 0.14-11.5 m center dot km(-1)), and daily average discharge (Q, 0.09- 634 m(3 center dot)s(-1)). A catchment-scale metric of surface water transit time (T-w, L(max)v(dye)(-1)) ranged from 0.3 to 40 days, averaging 7.2 days. A bivariate regression model using log(10) A and log(10) Q explained 83% of the variation in log(10) T-w and predicted T-w with an average precision of +/- 49%. By contrast, a previously published model based on hydraulic geometry relationships overestimated T-w by 100%. Application of my model to five streams nested in a ninth-order (omega = 9) catchment indicated that under dry (September) and wet (March), long-term (1954-2001) median flow conditions, v(w) increased with Q (v(w) Q(0.3)) as far downstream as omega = 8 and then remained constant or declined. The slope of this longitudinal v(w)-Q relationship was three times greater than the expected value. Longitudinal velocity gradients in many streams may thus be much steeper than commonly assumed.