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

Abstract

Estimates of average water velocity (vw) extracted from tracer dye studies (vdye) or calculated from velocity–discharge relationships at continuous-flow gauges (vgage) 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 km2), mainstem length (Lmax, 15.6–867 km), slope (S, 0.14–11.5 m·km–1), and daily average discharge (Q, 0.09–634 m3·s–1). A catchment-scale metric of surface water transit time (Tw, Lmaxvdye–1) ranged from 0.3 to 40 days, averaging 7.2 days. A bivariate regression model using log10 A and log10 Q explained 83% of the variation in log10 Tw and predicted Tw with an average precision of ±49%. By contrast, a previously published model based on hydraulic geometry relationships overestimated Tw by 100%. Application of my model to five streams nested in a ninth-order (ω = 9) catchment indicated that under dry (September) and wet (March), long-term (1954–2001) median flow conditions, vw increased with Q (vw ∝ Q0.3) as far downstream as ω = 8 and then remained constant or declined. The slope of this longitudinal vw–Q relationship was three times greater than the expected value. Longitudinal velocity gradients in many streams may thus be much steeper than commonly assumed.