Estimating relative bed-load contributions by lithology counts |
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| Authors: | Hugh H Mills and Paul J Tsai |
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| Institution: | (1) Department of Earth Sciences, Tennessee Technological University, 38501 Cookeville, Tennessee, USA;(2) Computer Center, Tennessee Technological University, 38501 Cookeville, Tennessee, USA |
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| Abstract: | In gravel-bedded streams where bed material of a tributary differs distinctly in lithology from that of the main stream, rock-type percentages can be used to estimate bed-load contributions of the two streams. The rock type that shows the greatest difference in abundance between the two streams is selected as the indicator lithology. Percentages of this lithology are estimated in both the main stream and tributary stream above their junction, and also in the main stream at a distance sufficiently downstream from the junction to allow complete mixing. The fraction of bed load contributed by the main stream, p,is estimated by
,where
is an estimate of the proportion of indicator rock fragments in the bed of the main stream above the junction,
is an estimate of the proportion in the bed of the tributary above the junction, and
is an estimate of the proportion in the bed of the main stream below the junction. The variance of
is obtained as var (
)= p1q1(pr – p2)2/n(p1 – p2)4] + p2q2(pr – p1)2/n(p1 – p2)4] + prqr/n(p1 – p2)2].Although no estimate of actual quantity of bed load is provided, the indicator rock technique supplies data that can serve as a check on data obtained by means of empirical formulas or actual transport measurements. |
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| Keywords: | lithology counts natural tracers bed-load transport binomial urn model |
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