Articles | Volume 20, issue 7
Hydrol. Earth Syst. Sci., 20, 2899–2912, 2016

Special issue: Geomorphometry: advances in technologies and methods for Earth...

Hydrol. Earth Syst. Sci., 20, 2899–2912, 2016

Research article 19 Jul 2016

Research article | 19 Jul 2016

On the propagation of diel signals in river networks using analytic solutions of flow equations

Morgan Fonley1,2,4, Ricardo Mantilla2,3, Scott J. Small2, and Rodica Curtu1 Morgan Fonley et al.
  • 1Department of Mathematics, University of Iowa, Iowa City, Iowa, USA
  • 2Iowa Flood Center, IIHR Hydroscience and Engineering, University of Iowa, Iowa City, Iowa, USA
  • 3Department of Civil and Environmental Engineering, University of Iowa, Iowa City, Iowa, USA
  • 4Department of Mathematics, Alma College, Alma, Michigan, USA

Abstract. Several authors have reported diel oscillations in streamflow records and have hypothesized that these oscillations are linked to evapotranspiration cycles in the watershed. The timing of oscillations in rivers, however, lags behind those of temperature and evapotranspiration in hillslopes. Two hypotheses have been put forth to explain the magnitude and timing of diel streamflow oscillations during low-flow conditions. The first suggests that delays between the peaks and troughs of streamflow and daily evapotranspiration are due to processes occurring in the soil as water moves toward the channels in the river network. The second posits that they are due to the propagation of the signal through the channels as water makes its way to the outlet of the basin. In this paper, we design and implement a theoretical model to test these hypotheses. We impose a baseflow signal entering the river network and use a linear transport equation to represent flow along the network. We develop analytic streamflow solutions for the case of uniform velocities in space over all river links. We then use our analytic solution to simulate streamflows along a self-similar river network for different flow velocities. Our results show that the amplitude and time delay of the streamflow solution are heavily influenced by transport in the river network. Moreover, our equations show that the geomorphology and topology of the river network play important roles in determining how amplitude and signal delay are reflected in streamflow signals. Finally, we have tested our theoretical formulation in the Dry Creek Experimental Watershed, where oscillations are clearly observed in streamflow records. We find that our solution produces streamflow values and fluctuations that are similar to those observed in the summer of 2011.

Short summary
We design and implement a theoretical experiment to show that, under low-flow conditions, observed streamflow discrepancies between early and late summer can be attributed to different flow velocities in the river network. By developing an analytic solution to represent flow along a given river network, we emphasize the dependence of streamflow amplitude and time delay on the geomorphology of the network. We also simulate using a realistic river network to highlight the effects of scale.