The dynamic reference frame of rivers and apparent transience in incision rates

Incision rates derived from river terraces are commonly used to infer rock uplift rates; however, an apparent dependence of incision rate on measured time interval may confound directly relating incision to uplift. The time-dependent incision rates are a Sadler effect that have been argued to result from a stochastic distribution of hiatal intervals in river incision, potentially reducing the utility of incision records for interpreting unsteadiness in tectonic processes. Here we show that time-dependent incision rates can arise from a simple systematic bias in the distance measurement used to calculate incision rate, and thus stochastic causes are not required. We present a conceptual model that describes the dynamic history of streambed elevation over cycles of terrace formation, illustrating that measured incision rate is time dependent because the stream channel reference frame is not fixed with respect to the geoid. Because it is challenging to reconstruct the full elevation history for a river channel, most researchers use the modern streambed elevation as a reference datum, but we demonstrate that doing so imposes a bias that manifests as an apparent dependence of rate on measured time interval. Fortunately, correction of this bias is straightforward, and allows river incision data to be used in studies of tectonic or climatic unsteadiness. INTRODUCTION Landscapes reflect the competition between processes of rock uplift and erosion. In nonglaciated regions where tectonics build mountains, river incision is the dominant mechanism governing landscape denudation (Howard et al., 1994; Whipple, 2004). Over long time scales (>106 yr) with steady tectonic forcing, river gradients will adjust so that rates of bedrock incision equal rock uplift rates (Merritts and Vincent, 1989; Snyder et al., 2000). In these settings, river terraces are commonly used to quantify incision and infer rock uplift (Pazzaglia, 2013). However, river incision is not a steady process, as climatic, autogenic, and/or stochastic (e.g., mass-wasting) processes modulate discharge and sediment supply, resulting in periods of bedrock erosion and times of lateral planation and/ or channel aggradation where vertical incision is negligible (Bull, 1991; Korup, 2006). It is this alternation between vertical incision and lateral planation or deposition that produces the river terraces from which incision histories can be derived (Pazzaglia and Brandon, 2001; Hancock and Anderson, 2002; Wegmann and Pazzaglia, 2002, 2009). Interpreting rates of rock uplift from the noise of unsteady incision remains a challenge in tectonic geomorphology studies. The dependence of process rate on measured time interval has long been recognized in geological phenomena and is commonly referred to as the Sadler effect (Sadler, 1981; Schumer and Jerolmack, 2009). Computation of the power-law relationship between measured distance and time interval is a test normally used to identify the Sadler effect, while avoiding autocorrelation when plotting rate versus its own denominator (Gardner et al., 1987; Mills, 2000; Finnegan et al., 2014). In such cases, the Sadler effect is functionally any significant deviation from unity in the power-law exponent (b) of log duration versus log distance. The mechanisms that give rise to the Sadler effect are still a matter of investigation. Most researchers follow Sadler’s (1981) postulation that it arises due to intermittency in hiatal or depositional intervals (Schumer and Jerolmack, 2009). Many argue that the Sadler effect is related to a stochastic, heavy-tailed distribution of hiatal intervals in sediment deposition (Jerolmack and Paola, 2010) or river incision (Finnegan et al., 2014); however, Sadler (1981) showed that deterministic and cyclic forcing can also give rise to the effect. An apparent dependence of rate on measured time interval is observed for river incision records on time scales approaching 107 yr (Mills, 2000; Finnegan et al., 2014). If it is confirmed that this fluvial Sadler effect is the result of stochastic hiatal intervals in river incision, the relationship between incision rate and rock uplift rate is unclear, and interpretations of tectonic unsteadiness are suspect (Finnegan et al., 2014). Although relatively well explored for stratigraphic records (Schumer and Jerolmack, 2009; Jerolmack and Paola, 2010), the exact processes that result in stochasticity of river incision over such broad time scales and across a diverse array of geologic and climatic environments remain speculative. For example, the impact of autocyclic factors (Finnegan and Dietrich, 2011) and stochastic processes, such as mass wasting (Korup, 2006) and extreme events like earthquakes and large storms (Wegmann and Pazzaglia, 2002; McPhillips et al., 2014), on long-term (106–107 yr) rates of river incision have not been conclusively demonstrated. Furthermore, such explanations do not address numerous observations in support of links between quasi-cyclic, deterministic climate forcing, and the formation of river terrace sequences, which can also account for time-dependent incision rates (Bull, 1991; Pazzaglia and Brandon, 2001; Hancock and Anderson, 2002; Pederson et al., 2006, 2013; Wegmann and Pazzaglia, 2009). Here we question whether the fluvial Sadler effect necessarily has anything to do with the temporal distribution of hiatal intervals, and explore alternative mechanisms that may give rise to time-dependent incision rates. CONCEPTUAL FRAMEWORK AND MODEL DESIGN It is necessary to distinguish between the process of river incision, which is erosion of the substrate (alluvium or bedrock) that floors a valley, and the measurement of incision, which is typically taken as the elevation difference between a terrace and the streambed. To avoid confusion of these two terms, we refer to the process of incision as erosion and the measurement of incision as incision or cumulative incision. We begin with a conceptual model that describes the elevation history of a streambed at a given point on a river long profile, in a landscape undergoing steady rock uplift (Fig. 1A). Over the long term (106–107 yr), the river profile is assumed to be in steady state, such that the rate of river erosion equals rock uplift and the profile does not move up or down with respect to the geoid. On shorter time scales (103–105 yr) the river alternates between bedrock erosion and channel aggradation or lateral planation, when downward erosion is negligible, in response to changes in discharge and sediment supply (Hancock and Anderson, 2002; Wegmann and Pazzaglia, 2002). Streambed elevation rises during intervals of sedi*Current address: Geological Institute, ETH Zurich, No E 31, Sonneggstrasse 5, 8092 Zurich, Switzerland. GEOLOGY, July 2015; v. 43; no. 7; p. 1–4 | Data Repository item 2015217 | doi:10.1130/G36692.1 | Published online XX Month 2015 © 2015 eological Society of A erica. For permission to copy, contact [email protected]. as doi:10.1130/G36692.1 Geology, published online on 26 May 2015