Getting Beyond the Bankfull Shields Parameter: A Continuum of Threshold Channel Types Illustrated by the Case of the White Clay Creek, PA

The Shields parameter based on median grain size D50 and bankfull depth is often used to interpret river morphology, but it may not always be a useful index of sediment transport processes. At 12 sites of the White Clay Creek (WCC), PA, the ratio of bankfull Shields stress to threshold Shields stress averages 1.41 (range 0.41-2.63), suggesting that these channels are alluvial near-threshold gravel-bed rivers. However, field mapping indicates confinement by bedrock and colluvium, and a channel slope dominated by bedrock incision and knickpoint migration. A numerical model of WCC bed material transport and grain size, calibrated to bedload tracer data, demonstrates that 22% (range 8-73%) of the bed material is composed of a population of immobile cobble and boulder-sized sediment supplied through local colluvial processes and bedrock erosion, and a separate population of mobile sand, pebbleand cobble-sized alluvium. Computations also suggest that channel morphology is only weakly coupled to upstream sediment supply. Additional analyses further imply that width adjustment may reflect a balance between cohesive bank erosion and floodplain deposition, though channels nonetheless may be closely scaled by cohesive bank erosion thresholds. WCC represents an example of a continuum of underappreciated, but relatively common, threshold alluvial-colluvial-bedrock rivers with partially immobile beds and widths scaled by cohesive bank erosion thresholds. Fluvial geomorphologists will need to look beyond simple sediment transport metrics to fully understand and classify these stream channels.

This study that the stream bed is fully mobile at bankfull stage and that gravel stability plays a role 116 in width adjustment. 117 The study described here presents an analysis of fluvial processes and morphology 118 designed to test these hypotheses. We observed event-scale bedload transport processes 119 and document the geomorphic setting, morphology, and stratigraphy of river reaches through-120 out the watershed. We use a numerical model of bedload transport, calibrated to local 121 conditions, to assess the mobility of individual grain size fractions and to determine the 122 sensitivity of channel morphology to the supply of bed material. These data motivate 123 us to propose a new, but arguably common, category of threshold river behavior that 124 we term the alluvial-colluvial-bedrock threshold channel (Table 1).   (Hack, 1982;Reed, 1981). The Fall Zone has been alternatively 146 interpreted as a hinge point for ongoing Cenozoic crustal warping (Hack, 1982  fluenced by colonial and more recent watershed disturbances. Grain sizes exposed on the 157 streambed range from sand to boulders; cobbles, pebbles, and sand appear to be sup-158 plied through sediment transport from upstream, while boulders and cobbles are sourced 159 locally from colluvium and exposed bedrock. Eroding streambanks are common, sup-160 plying sediment ranging from clay to cobble-sized gravel. Mobile bed material is stored 161 in lateral bars, and, to a lesser extent, on a coarse-grained bed that appears to be partly 162 anchored by immobile cobbles and boulders. Sediment stored in bars appears to be mo- fully alluvial channel, but should rather be considered a mixed bedrock-alluvial chan-169 nel. Furthermore, if the supplied gravel bed material mostly behaves as throughput load, 170 then channel morphology should be insensitive to changes in the supply of bed material.

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Additionally, changes in bed material supply should be readily accommodated by changes 172 in the grain size of stored bed material, rather than changing morphology, as would be 173 expected for alluvial channels.

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Field observations across multiple scales and bedload transport computations pro-175 vide data to test and refine our preliminary conceptual model for the White Clay Creek.  Creek. Immobile cobbles and boulders are supplied locally through bank erosion and channel incision, while the fluvial supply from upstream consists of sand and pebbles stored in bars. The streambed is anchored by cobbles and boulders that are immobile at bankfull stage, but contains a sparse covering of throughput load consisting of sand and pebbles primarily supplied from upstream (but augmented by locally eroding banks).
determine the sensitivity of the channel of the White Clay Creek to changes in the sup-188 ply of bed material.   Table 2). Five of the sites have side 201 channels or well-developed mid-channel bars, while the remainder are single-thread chan-202 nels. Most of the sites are sinuous (sinuosity < 1.5), but two sites have sinuosities in ex-203 cess of 1.5 and could be considered meandering (Table 2). Bedrock and colluvium bor-  The stratigraphic setting was documented through measurements and observations 222 of deposits exposed in eroding banks, and also by creating a geologic cross-section at Site   The tracers were installed in situ on the streambed by drilling holes into clasts that 242 were exposed above the surface of the water at low flow. The RFID tags were placed in 243 the holes and sealed in place with a waterproof epoxy. Tags were installed in situ wher-244 ever possible in order to prevent our actions from disturbing the bed and increasing the 245 likelihood of transport. In order to tag clasts that were underwater, the waterproof epoxy 246 was used as a glue to attach a tag to the surface of each clast. If clasts were sufficiently 247 small (1-5 cm), the tag could not be affixed without disturbing the bed. These small clasts 248 were removed from the streambed in order to attach the RFID tag.  [m] [-] [-] [-] [-] [-] [-] [-] [   To assess bedload transport at the various study reaches, we use the sediment trans- the data collected in this study are poorly suited to previous methods. Here we define 288 the reference shear stress (τ ri ) for a particular particle as the stress that is associated 289 with a transport distance of a single grain diameter.

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The shear stress generated by each flow event was determined by correlating the 291 measured depth in the study reach (determined by the high water mark surveys and cross-292 sectional surveys) to the gage height at the downstream Strickersville gage. It is assumed 293 that the highest flow event prior to each survey was responsible for mobilizing all bed-294 load tracers. By relating the shear stress of the flow events to bedload tracer mobility, 295 a range of reference shear stresses for each grain size category (τ ri ) could be determined.

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A relationship between grain size and average reference shear stress could then be as-297 certained for all grain sizes, even those too small to tag or too large to be mobilized by 298 conditions observed during the study period. Thus, two important parameters were found-299 the reference shear stress for the mean grain size (τ rm ) and the hiding function expo-300 nent (b), which are utilized in the following hiding function: where τ rm is the reference shear stress for the geometric mean grain size (D m ), τ ri is Due to the range of reference shear stresses found for each grain size category, a 309 5% and 95% confidence interval was used to find the upper and lower range of the ref- 310 erence shear stress and the hiding function exponent. The hiding function, which increases 311 the mobility of large grain sizes that have a greater surface area exposed to the flow and 312 reduces the mobility of smaller grain sizes that tend to be hidden amongst larger clasts, 313 has the ability to significantly alter the outcome of the sediment transport model. We  We did not assess differences in shear stress associated with complex bar topography at   (Parker, 1991(Parker, , 2008: where λ p is the porosity of the bed (set equal to 0.3), L a is the thickness of the active 350 layer, F bi is the fraction of grain size i on the bed, F li is the fraction of grain size i at 351 the interface between the active layer and the subsurface, q bi is the volumetric bed ma-352 terial transport rate per unit width, t is time, and x is the downstream spatial coordi-353 nate. In solving equation (2), differential terms are represented by finite differences. For 354 example, the term on the right is approximated as (q bi out q bi in )/dx, where q bi in is the 355 specified supply of grain size i from upstream, q bi out is the transport out of the study and bedload, such that F li = aF bi + (1 − a)p i , where p i is the fraction of grain size i 362 in the bedload and a is an exchange parameter (set equal to 0.7).

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Once fractional transport rates have been computed by solving equation (2), they 364 are summed to determine the total bed material flux, q b T otal . Changes in bed elevation, 365 z b , over time are then determined by solving equation (3) (Parker, 1991(Parker, , 2008: Numerical experiments were designed to test two key hypotheses of our conceptual Creek to transport bed material, and (2) the grain size distribution of the bed material 371 reflects the grain sizes supplied from upstream in addition to grain sizes supplied locally.

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To test these hypotheses, computations proceed in the following manner. First, the ex-  ∆z b = L a , ∆z b > L a Alluvial conditions reached; bed has aggraded to cover non-alluvial material 0 < ∆z b < L a Alluvial-colluvial-bedrock channel persists with some aggradation ∆z b < 0 Alluvial-colluvial-bedrock channel persists with some erosion of bed material Mean grain size, D m   a Sand-sized sediment (< 2mm) was excluded from the grain size distribution when determining median grain size. This is because sand-sized sediment is expected to be transported in suspension during bankfull flows. b NA-not applicable. c ND-no data: some study sites lacked a well-developed gravel bar.     [mm] [mm] [mm] [mm] [mm] [%] [%] [%] Note. The largest mobile grain size is determined using the Wilcock and Crowe (2003) sediment transport equation that has been calibrated to conditions at the bedload tracer study site. The range of largest mobile grain sizes is based on the range of hiding function exponents (b = 0.93 and b = 0.61) determined by the 5% and 95% confidence interval of the bedload tracer mobility data.
a Sand-sized sediment (< 2mm) was included in the grain size distribution when determining mean size. b ND-no data; some study sites lacked a well-developed gravel bar. c Average for all 12 study sites. d Average for 8 study sites with well developed gravel bars present (Site 1, 2, 3, 4, 5, 6, 8, 12, 14) -19-manuscript submitted to JGR: Earth Surface 1998; Millar & Quick, 1993. Near-threshold alluvial gravel-bed rivers adjust their 571 morphology to achieve erosion thresholds for gravel at the bank toe (Parker, 1978).

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Eroding banks occur frequently along the White Clay Creek (Table 1) It has been noted, however, that even laterally active channels, if appropriately av- where E is a dimensionless erodibility coefficient (Pizzuto & Meckelnburg, 1989). Fol- migrating slowly (as is typical for the White Clay Creek), then the rate of lateral accre-606 tion will be low, and the ratio L A /EU c is will be 1, because L A is scaled by the dif-607 ference U b U c , rather than the velocity itself. Under these conditions, the quantity in paren-608 theses on the right of equation (7) will be only slightly greater than one, allowing for chan-609 nel width to be only slightly greater than the threshold width and the width itself to scale 610 -22-manuscript submitted to JGR: Earth Surface with the bank erosion threshold velocity U c . Equation (7) also provides a mechanism for width to vary with discharge, allowing for downstream hydraulic geometry relationships 612 such as those presented for the nearby Brandywine Creek by Wolman (1955).

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This analysis is not intended to be either comprehensive or precise, and it is ad-614 mittedly simplistic and speculative. The assumption of an equilibrium width, for exam-615 ple, is difficult to justify given the dramatic changes to watersheds of the region outlined 616 below. Equation (7), however, does present a hypothesis to explain how width scaling 617 by cohesive bank erosion thresholds could arise even when channels are laterally active, 618 thereby providing a link between the White Clay Creek and proposed scaling of alluvial 619 sand-bed and gravel-bed channels by cohesive bank erosion thresholds. Further research 620 is clearly warranted, of course, to more fully test these ideas. Creek (illustrated in Figure 3). These deposits create a variety of surfaces representing 634 differing elevations, depositional processes, and periods in the history of the White Clay

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Creek. For example, in Figure 3b, the thickness of the deposits on the right side of the  Creek is composed of two populations of sediment, analyses based on a single grain size 667 such as the bankfull Shields stress scaled by D 50 are unlikely to be useful, motivating 668 a more thorough analysis of sediment transport processes by that incorporates the mo-669 bility of individual grain size fractions.

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By expanding our analysis beyond bedload transport processes to include bank stratig- Creek is not only a threshold channel because some of its bed material is near the thresh-673 old of motion at bankfull stage, but its width may also be scaled by cohesive bank ero-674 sion processes. We argue that even though banks cannot be precisely adjusted to bank