Formation of Fluvial Hanging Valleys: Theory and Simulation

Although only recently recognized, hanging tributary valleys in non-glacial landscapes are not uncommon in tectonically active regions. Standard river incision models do not allow for the formation of fluvial hanging valleys; these disequilibrium landforms present an opportunity to advance our understanding of river incision processes. In this work, we demonstrate that thresholds apparent in sediment-flux dependent bedrock incision rules provide mechanisms for the formation of hanging valleys in response to transient pulses of river incision. We simplify recently published river incision models in order to derive analytical solutions for the conditions required for hanging valley formation and use these results to guide numerical landscape evolution simulations. Analytical and numerical results demonstrate that during the response to base level fall, these incision rules may create either temporary or permanent hanging valleys. These hanging valleys form as a consequence of (1) rapid mainstem incision oversteepening the tributary junctions beyond a threshold slope or (2) tributary sediment flux response lagging behind the pulse of incision, temporarily limiting the tributary’s capacity to keep pace with the mainstem. The distribution of permanent and temporary hanging valleys results from four competing factors: the magnitude of base level fall, the upstream attenuation of the incision signal, the lag time of the sediment flux response and the non-systematic variation in tributary drainage areas within the stream network. The development of hanging valleys in landscapes governed by sediment-flux dependent incision rules limits the transmission of base level fall signals through the channel network, ultimately increasing basin response time. Crosby et al., submitted to JGR-ES Motivation Following a change in tectonic or climatic forcing, hillslopes and channels adjust their form as the landscape moves toward equilibrium with the new boundary conditions. The form and response time of this transient adjustment exerts a fundamental influence on the growth and development of mountain ranges, the timing and delivery of sediment to depositional basins and other fundamental processes in tectonically active landscapes. In non-glacial, tectonically active landscapes, it has recently been discovered that many tributary basins are observed “hanging” above their junction with the incised trunk stream [Crosby and Whipple, in press; Snyder, et al., 1999; Wobus, et al., in press]. The over-steepened channel reach, often referred to as a knickpoint, separates the relict hanging tributary basin from the incised, adjusting portion of the landscape (figure 1). We identify the Waipaoa River on the North Island of New Zealand as an excellent location to study knickpoint distribution within fluvial basins because of the known time of disturbance [Berryman, et al., 2000; Eden, et al., 2001] and the abundance of transient landforms such as terraces, incised inner gorges and knickpoints [Crosby and Whipple, in press]. Even with a field site as well constrained as the Waipaoa, we found it is difficult to discern whether hanging valley formation requires discrete knickpoints migrating up the mainstem to their present position or whether hanging valleys can develop in-place at tributary junctions when prolonged mainstem incision outpaces tributary adjustment [Crosby and Whipple, in press]. The presence and persistence of knickpoints at tributary junctions limits the upstream communication of subsequent signals of base level change into the upper portions of the channel network, thus extending basin response time following disturbance. The most broadly utilized formulation for fluvial bedrock incision, the detachment-limited stream power model [Howard, 1994; Howard and Kerby, 1983; Whipple and Tucker, 1999] (henceforth simply termed the stream power model), does not predict the formation of hanging tributaries[e.g. Niemann, et al., 2001]. This discrepancy between field observation and model behavior suggests a clear inadequacy in standard river incision models. Recently developed sediment-flux dependent bedrock incision relations allow sediment to behave either as a tool for incising the bed or as armor, inhibiting erosion [Gasparini, et al., 2006; Parker, 2002; Sklar and Dietrich, 1998; Sklar and Dietrich, 2004; Whipple and Tucker, 2002]. We find that these relations provide mechanisms for explaining the formation and persistence of hanging tributaries at threshold drainage areas [Crosby and Whipple, in press; Gasparini, et al., submitted; Wobus, et al., in press]. In particular, the prevalence of hanging tributaries in tool-starved environments may provide the strongest existing field evidence for the applicability of sediment-flux dependent incision rules and their clear superiority to standard detachment-limited and transport-limited stream power models. Approach and Scope In this work, we utilize analytical and numerical models to explore whether thresholds in existing relations for stream incision by sediment abrasion provide a plausible mechanism for the formation of hanging valleys. The theoretically demonstrated consequences of these thresholds are then considered