Modeling Decadal Bed Material Sediment Flux Based on Stochastic Hydrology
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UC Santa Barbara UC Santa Barbara Previously Published Works Title Modeling decadal bed material sediment flux based on stochastic hydrology Permalink https://escholarship.org/uc/item/0x44f33j Journal Water Resources Research, 40(3) ISSN 0043-1397 Authors Singer, M B Dunne, T Publication Date 2004-03-01 DOI 10.1029/2003WR002723 Peer reviewed eScholarship.org Powered by the California Digital Library University of California WATER RESOURCES RESEARCH, VOL. 40, W03302, doi:10.1029/2003WR002723, 2004 Modeling decadal bed material sediment flux based on stochastic hydrology Michael Bliss Singer and Thomas Dunne Donald Bren School of Environmental Science and Management, University of California, Santa Barbara, California, USA Received 3 October 2003; revised 28 December 2003; accepted 9 January 2004; published 18 March 2004. [1] Estimates of decadal bed material sediment flux and net storage are derived by driving sediment transport calculations with a stochastic hydrology model. The resulting estimates represent the whole distribution of sediment flux based on natural variability in channel characteristics (gradient, width, and bed grain size) and the magnitude, duration, and interarrival time of flood events. A procedure for calibrating a fractional sediment transport equation of a commonly used form to bed material grain size distributions (BMGSDs) at cross sections is presented. The procedure was applied to the Sacramento River channel network to compute estimates of annual total and annual peak bed material discharges into and through the main stem over a 30-year period. Main stem bed material budgets were evaluated to identify reaches in states of net accumulation or scour. Simulations highlight large imbalances in sand and gravel storage throughout the Sacramento River, which can be explained by a combination of local hydraulics and BMGSDs and for which there is at least some empirical support. INDEX TERMS: 1815 Hydrology: Erosion and sedimentation; 1869 Hydrology: Stochastic processes; 1821 Hydrology: Floods; KEYWORDS: bed material transport, sediment budgets, stochastic simulation, Sacramento River Citation: Singer, M. B., and T. Dunne (2004), Modeling decadal bed material sediment flux based on stochastic hydrology, Water Resour. Res., 40, W03302, doi:10.1029/2003WR002723. 1. Introduction and other rivers, and connected it to HYDROCARLO, a stochastic model of streamflow in a channel network (M. B. [2] Bed material flux is the transport of sediment that constitutes the riverbed. The variation in bed material flux Singer and T. Dunne, An empirical-stochastic, event-based along a river channel creates a spatial pattern of stored model for simulating inflow from a tributary network: sediment. These storage patterns influence the formation of Theoretical framework and application to the Sacramento the channel (e.g., point bars) and its functioning (e.g., depth River basin, California, submitted to Water Resources of flow over a portion of a cross section). Accordingly, Research, 2003) (hereinafter referred to as Singer and sediment storage can be thought of as the prime determinant Dunne, submitted manuscript, 2003). We used the coupled of channel morphology in alluvial channels and thus of models to estimate the frequency distributions, including the flood conveyance and habitat conditions in a river reach. extrema and central tendency, of bed material discharge in various grain size classes over a period of decades. We [3] Long-term estimates of bed material sediment flux and storage in large rivers are required for various purposes applied this method at various cross sections along the main ranging from applications in flood control (bed elevations) stem Sacramento River and at the mouths of its major and river rehabilitation to research on sediment budgets and tributaries, and thus developed a basinwide method for channel morphology. These estimates are generally reported assessing the long-term influence of flood variability on as single values derived from sediment transport data with bed material transport. To our knowledge, our decadal no assessment of the uncertainty in their calculation [e.g., estimation of the spatial variability of sediment transport Milliman and Meade, 1983; Milliman and Syvitski, 1992] or at large basin scale is unprecedented. their inter-annual variation. Dunne et al. [1998] applied [5] Many studies have acknowledged the inaccuracies in error propagation to sediment rating curve analyses of bed sediment transport prediction arising from uncertainty in material and washload fluxes and reach accumulations in hydraulic variables [McLean, 1995], spatial distribution of the Amazon basin. McLean et al. [1999] reported a 20-year bed shear stress [Wilcock, 1996], and assessment of critical record of bed load in a large gravel bed river with error shear stress [Wilcock, 1992; Buffington and Montgomery, analyses of measurements and rating curves. However, to 1997]. Additionally, variations in local bed material grain our knowledge, there have been no attempts to represent size distributions (BMGSDs) due to patch dynamics [e.g., inter-annual variability in load estimates specifically due to Paola and Seal, 1995] or topographic variability across the the hydraulics of a variable flow regime. stream control initial mobility of sediment, the quantity of each size available for transport, and thus transport rates. [4] Toward this end, we have calibrated a bed material transport formula with measurements from the Sacramento However, streamflow is an additional source of uncertainty introduced when one tries to obtain a decadal estimate of bed material flux. The sensitivity of bed material flux to stream- Copyright 2004 by the American Geophysical Union. flow is apparent in regressions of the logarithm of bed 0043-1397/04/2003WR002723$09.00 material flux on the logarithm of stream discharge, which W03302 1of14 W03302 SINGER AND DUNNE: MODELING DECADAL BED-MATERIAL FLUX W03302 generally result in exponents greater than one. Even if one Mount Shasta through the northern Central Valley to the could properly constrain each of the aforementioned varia- San Francisco Bay-Delta in California. It is controlled at the bles for a given set of flow conditions, it would still be northern end by Shasta Dam, built in 1943. The Sacramento necessary to properly characterize the stochastic frequency, exhibits a range of fluvial environments. From Shasta Dam, magnitude, and duration of flow at a given cross section, in it winds southward through Sacramento Canyon, incises order to obtain an appropriate estimate of long-term bed into Pleistocene deposits on the Redding plain, and arcs material flux. Such a strategy is particularly important to through Iron Canyon to Bend Bridge (BB in Figure 1). This determine the role of floods and their management in part of the river, labeled reach 0 (Figure 1), is 40 km in sediment transport and channel formation, and for assessing length, has a bed of sandy gravel (25% sand in bed riverine habitat condition. The influence of historical stream- material at BB), width of 150 m, slope of 8.9 Â 10À4, flow on sediment transport estimates has been assessed and point bar topography. From corroborated (K. Buer, empirically by convolving bed load ratings with flow fre- CDWR, personal communication) field observations, we quency curves [McLean et al., 1999]. We build on this determined that 50% of the bed in reach 0 consists of the research by stochastically simulating a range of flows and erosion-resistant Tehama formation. South of Bend Bridge assessing their influence on decadal bed material transport. the Sacramento enters the Central Valley, where it meanders [6] Long-term sediment flux prediction that incorporates across a wide floodplain through Pleistocene river gravels to the real variability inherent in the hydrology of a fluvial Hamilton City (HC). Reach 1 is 60 km in length, with a system would be useful on the scale of a cross section where gravel and sand bed (40% sand at HC), width of 200 m, computations are made (e.g., to evaluate local adjustment to and slope of 5.4 Â 10À4, with shallow cross sections and a rehabilitation strategy) and that of a basin as a whole (e.g., 2 m natural levees. Downstream of Hamilton City, the to assess a the influence of system-wide perturbations on the Sacramento continues meandering through the valley, but is sediment budget). In order to design a gravel augmentation partially constrained by flood control levees, which influ- strategy on the local scale, for example, it would be useful ence the river’s course beginning upstream of Butte City to quantify the central tendency and extrema of spawning- (BC). Reach 2 is 30 km in length, consists of similar bed sized gravel transport past a particular cross section. On the material (49% sand at BC), cross-sectional topography, basin scale, it would be useful to assess the influence of and width as reach 1, but with a lower slope (2.5 Â 10À4). land-use change (e.g., an increase in sand loading to the Below Butte City the Sacramento enters a reach where flood channel) on bed material transport in various grain sizes control levees are set back 1 km from the channel until throughout the main stem. This paper outlines a basinwide Colusa (CO). Reach 3 is 25 km in length, consists of a method for quantifying the variations in bed material sand bed (75% sand at CO), width and cross sectional transport over a period of decades punctuated by flood topography similar to the upstream reaches, and a slope of events