## 1 Introduction

Steep mountain streams are energetic systems that transport significant volumes of sediment and are often the source of the majority of the coarse sediment load within a basin. Sediment fluxes in these environments are an integral part of the transfer of sediment from source areas to depositional settings, and so they influence bedrock incision rates [*Sklar and Dietrich*, 2004], channel morphology, and flood hazards [*Czuba et al.*, 2012a] and are a necessary piece of information in various river engineering and restoration activities. The intense rates of transport may also constitute a significant natural hazard for local communities and infrastructure. To date, predicting mountain stream sediment fluxes remains difficult. Our current understanding of sediment transport, developed primarily in low-gradient rivers and laboratory flumes, does not necessarily transfer to these environments, and sediment transport equations often mispredict transport rates by several orders of magnitude [*Rickenmann*, 2001]. This poor performance has been variously explained as a failure to account for the increased form drag losses in steeper streams [*Chiari and Rickenmann*, 2007; *Nitsche et al.*, 2011] or the increasing critical shear stresses observed with increasing slopes [*Mueller et al.*, 2005; *Lamb et al.*, 2008]. More broadly, the relative lack of accurate measurements of sediment transport rates in steep streams hampers our ability to develop empirical relations for these environments. Direct measurements of sediment transport, and particularly the geomorphically significant bed material fraction, are complicated by the energetic transport of coarse sediment and the logistical difficulties of making such measurements at remote sites during episodic events.

In recent decades, the increased resolution and availability of topographic surveys has presented the possibility of quantifying sediment fluxes through the analysis of repeat measurements. This method, referred to as morphologic budgeting, assumes that sufficiently accurate measurements of landscape change should provide estimates of accumulated transport rates, given simple conservation of mass. The idea is not a new one, having been suggested in the context of fluvial transport as early as the early 1960s and 1970s [*Popov*, 1962; *Neill*, 1971] and used with some success along the Fraiser River in the late 1990s [*McLean and Church*, 1999]. However, modern survey techniques have significantly increased the potential accuracy and extent of morphologically based transport estimates and have recently been used to quantify fluxes in landslides [*DeLong et al.*, 2012], debris flows [*Schürch et al.*, 2011], and fluvial transport [*Lane et al.*, 2003; *Wheaton et al.*, 2010; *Croke et al.*, 2013]. These methods are particularly well suited to the quantification of transport in energetic settings or during extreme events, in which the scale of geomorphic change is generally large and where more direct measurements of transport are often inaccurate, unsafe, or otherwise untenable.

In this work, we present an application of morphologic budgeting methods in which repeat aerial lidar surveys are used to estimate sediment fluxes down the length of Tahoma Creek, a steep, proglacial stream located on the southwest flank of Mount Rainier, Washington (Figure 1). We use surveys acquired in 2002, 2008, and 2012 to estimate accumulated volumetric transport over the two time intervals between surveys, the earlier of which includes the effects of a massive flood in November 2006. We then present a method by which these accumulated loads, in combination with discharge records, may be used to estimate sediment rating curves. This is accomplished by noting that our accumulated transport volumes can be described as the integral of transport rates over the relevant time periods and, in turn, that transport rates may be described as a monotonic, continuous function of discharge. With two independent time periods, we are able to write two equations of the form , where AL is the accumulated sediment load measured from our lidar surveys and *f*(*Q*) is an unspecified function describing the relationship between discharge and sediment transport rate. Positing that *f*(*Q*) takes the form of a power law, *a**Q*^{b}, we can use these two equations to numerically solve for the unique values of *a* and *b* that correctly predict our lidar-derived estimates of accumulated transport over both time periods. These values of *a* and *b* then provide temporarily continuous estimates of transport rates at the resolution of our discharge records and may be used to estimate transport for time periods outside of our survey intervals. Finally, we use both our estimates of accumulated transport and our derived rating curve to assess the skill of several bed load transport equations applied to the steep settings of Tahoma Creek.

We present these analyses in two broad sections: the first entails the methods and results of our lidar analysis, as well as an assessment of those results, and the second section then presents the methods by which we used our lidar results to assess transport equations and the results of that assessment. The subsequent discussion and conclusions encompass both sections.