Sediment supply controls equilibrium channel geometry in gravel rivers

Abstract

<p id="d6932897e156">Geomorphologists commonly assume that gravel-bedded rivers tend toward a “threshold” equilibrium state, in which the median-sized grains on the riverbed surface begin to move at the bankfull flood stage. However, here we show that this widely held assumption fails to capture a more fundamental pattern in river channel geometry. Our findings provide evidence that river channel geometry and grain size are inherently linked to the supply of sediment transported from upstream. Threshold channels may therefore simply reflect settings with low sediment supplies, while high sediment supply channels are adjusted to transport large volumes of material during bankfull floods. Thus, an understanding of sediment supply is key to interpreting, predicting, and restoring bankfull geometry in rivers. </p><p class="first" id="d6932897e159">In many gravel-bedded rivers, floods that fill the channel banks create just enough shear stress to move the median-sized gravel particles on the bed surface ( <i>D</i> ₅₀). Because this observation is common and is supported by theory, the coincidence of bankfull flow and the incipient motion of <i>D</i> ₅₀ has become a commonly used assumption. However, not all natural gravel channels actually conform to this simple relationship; some channels maintain bankfull stresses far in excess of the critical stress required to initiate sediment transport. We use a database of &gt;300 gravel-bedded rivers and &gt;600 ¹⁰Be-derived erosion rates from across North America to explore the hypothesis that sediment supply drives the magnitude of bankfull shear stress relative to the critical stress required to mobilize the median bed surface grain size ( <span class="inline-formula"> <math id="i1" overflow="scroll"> <mrow> <mrow> <mrow> <msubsup> <mi>τ</mi> <mrow> <mi>b</mi> <mi>f</mi> </mrow> <mo>*</mo> </msubsup> </mrow> <mo>/</mo> <mrow> <msubsup> <mi>τ</mi> <mi>c</mi> <mo>*</mo> </msubsup> </mrow> </mrow> </mrow> </math> </span>). We find that <span class="inline-formula"> <math id="i2" overflow="scroll"> <mrow> <mrow> <mrow> <msubsup> <mi>τ</mi> <mrow> <mi>b</mi> <mi>f</mi> </mrow> <mo>*</mo> </msubsup> </mrow> <mo>/</mo> <mrow> <msubsup> <mi>τ</mi> <mi>c</mi> <mo>*</mo> </msubsup> </mrow> </mrow> </mrow> </math> </span> is significantly higher in West Coast river reaches (2.35, <i>n</i> = 96) than in river reaches elsewhere on the continent (1.03, <i>n</i> = 245). This pattern parallels patterns in erosion rates (and hence sediment supplies). Supporting our hypothesis, we find a significant correlation between upstream erosion rate and local <span class="inline-formula"> <math id="i3" overflow="scroll"> <mrow> <mrow> <mrow> <msubsup> <mi>τ</mi> <mrow> <mi>b</mi> <mi>f</mi> </mrow> <mo>*</mo> </msubsup> </mrow> <mo>/</mo> <mrow> <msubsup> <mi>τ</mi> <mi>c</mi> <mo>*</mo> </msubsup> </mrow> </mrow> </mrow> </math> </span> at sites where this comparison is possible. Our analysis reveals a decrease in bed surface armoring with increasing <span class="inline-formula"> <math id="i4" overflow="scroll"> <mrow> <mrow> <mrow> <msubsup> <mi>τ</mi> <mrow> <mi>b</mi> <mi>f</mi> </mrow> <mo>*</mo> </msubsup> </mrow> <mo>/</mo> <mrow> <msubsup> <mi>τ</mi> <mi>c</mi> <mo>*</mo> </msubsup> </mrow> </mrow> </mrow> </math> </span>, suggesting channels accommodate changes in sediment supply through adjustments in bed surface grain size, as also shown through numerical modeling. Our findings demonstrate that sediment supply is encoded in the bankfull hydraulic geometry of gravel bedded channels through its control on bed surface grain size. </p>