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

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.