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Earth Surface Dynamics An interactive open-access journal of the European Geosciences Union
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Discussion papers
https://doi.org/10.5194/esurf-2019-4
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/esurf-2019-4
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.

Research article 13 Feb 2019

Research article | 13 Feb 2019

Review status
This discussion paper is a preprint. It is a manuscript under review for the journal Earth Surface Dynamics (ESurf).

Estimating confidence intervals for gravel bed surface grain size distributions

Brett C. Eaton, R. Dan Moore, and Lucy G. MacKenzie Brett C. Eaton et al.
  • Geography, The University of British Columbia, 1984 West Mall, Vancouver, BC, Canada

Abstract. Most studies of gravel bed rivers present at least one bed surface grain size distribution, but there is almost never any information provided about the uncertainty of the percentile estimates. We present a simple method for estimating the confidence intervals about the grain size percentiles derived from standard Wolman or pebble count samples of bed surface texture. Our approach uses binomial probability theory to generate confidence intervals for all grain sizes in the distribution. We find that the standard sample size of 100 observations is associated with errors ranging from about ±15 % to ±30 %, which may be unacceptably large for many applications. In comparison, a sample of 500 stones produces an uncertainty ranging from about ±9 % to ±18 %. In order to help workers develop appropriate sampling approaches that produce the desired level of precision, we present simple equations that approximate the proportional uncertainty associated with the median size and the 84th percentile of the distribution as a function of the sample size and the standard deviation of the distribution, assuming that the underlying distribution is log-normal. However, the true uncertainty of any sample can only be accurately estimated once the sample has been collected, so these simple equations complement – but do not replace – the basic uncertainty analysis using binomial probability theory.

Brett C. Eaton et al.
Interactive discussion
Status: final response (author comments only)
Status: final response (author comments only)
AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment
Brett C. Eaton et al.
Data sets

bceaton/ESD2019_BCE_RDM_LGM: Data and Code B. C. Eaton, R. D. Moore, and L. G. MacKenzie https://doi.org/10.5281/zenodo.2551824

Model code and software

bicalc r package B. C. Eaton, R. D. Moore, and L. G. MacKenzie https://doi.org/10.5281/zenodo.2551826

Brett C. Eaton et al.
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Latest update: 17 Jul 2019
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Short summary
Researchers studying gravel bedded rivers almost always require a sample of the bed surface grain size range. These samples are typically expressed as cumulative frequency distributions. We present a technique for generating confidence intervals for the various size percentiles. This gives other researchers the ability to estimate the uncertainty of their samples, and to refine their sampling methods to achieve the desired level of precision.
Researchers studying gravel bedded rivers almost always require a sample of the bed surface...
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