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Durham University

Department of Earth Sciences


Publication details for Professor Fred Worrall

Worrall, F., Howden, N.J.K. & Burt, T.P. (2013). Assessment of sample frequency bias and precision in fluvial flux calculations – an improved low bias estimation method. Journal of Hydrology 503: 101-110.

Author(s) from Durham


Despite the importance of calculating the flux of solutes and particulates through the global fluvial network
the number of studies that have considered the bias and precision of any method is limited. Furthermore,
no study has, on the basis of the bias of the method, proposed new methods with a lower
bias nor considered the implications of the bias estimation for existing published studies. Using 3 years
of high frequency data (hourly) for dissolved organic carbon (DOC) this study systematically degraded the
data and recalculated the flux for varying sample frequencies and considered a range of interpolation,
ratio and extrapolation methods. The results show that:
(i) Interpolation and ratio methods showed a consistent, small bias for sampling frequencies up to
every 14 days, but bias rapidly increased for lower sample frequencies with the flux estimates
being between 40% and 45% of the ‘‘true’’ flux at 31 day (monthly) sampling.
(ii) The best ratio method was based upon correction against an unrealistic assumption that river flow
was normally distributed.
(iii) Extrapolation methods based on fixed sampling period monitoring proved to be erratic but no better
than interpolation methods.
Based upon the nature of the sources of variation within the flow and solute datasets we propose the following
method for calculating the fluvial flux (F) of a solute:
F ¼ KEðCiÞQtotal
where: Qtotal = the total flow in a year (m3/yr); E(Ci) = the expected value of the sampled concentrations
(mg/l); and K = a conversion factor. This new method preserved all the available flow information and
had a bias of as low as 8% for monthly sampling. When the method was applied to DOC flux from Great
Britain bias correction meant a 97% increase in the national flux over previous estimates.