Uncertainty of excess density and settling velocity of mud flocs derived from in situ measurements

Direct or indirect measurements of excess density and settling velocity are inherently associated with uncertainties (errors) due to a lack of accuracy of the measuring instruments, inadequate precision of the observations, and the statistical nature of the variables (floc size, primary particle size and primary particle density). When using observations, some understanding of the uncertainties is needed. Based on the theory of error propagation, we have estimated the error of the excess density and the settling velocity of mud flocs using the measurement data of OBS, SPM filtration, LISST 100C, CTD and Sedigraph. The measurements were carried out between 2003 and 2005 in the southern North Sea in the course of eight tidal cycles. The excess density was calculated based on fractal description of mud flocs and using floc and water density data. The water density was derived from CTD measurements and the floc density was calculated using SPM concentration, particle volume concentration, and water and primary particle densities. The settling velocities of flocs were calculated on the basis of their fractal structure following Winterwerp, J. [1998. A simple model for turbulence induced flocculation of cohesive sediments. Journal of Hydraulic Research 36, 309–326].The results show that the relative standard deviations for excess density, fractal dimension and settling velocity are about 10%, 2.5% and 100%, respectively. These uncertainties should be regarded as lower limits of the real error because the errors due to inaccuracies of the OBS, LISST and Sedigraph have been excluded, as they are unknown. From the results it was found that the statistical error of excess density was dominated by uncertainties of SPM concentration and primary particle density, and for fall velocity by uncertainties of primary particle and floc sizes, respectively. These statistical uncertainties will always be high when dealing with natural flocs or particles and cannot be reduced by increasing the accuracy of the instruments. They should therefore be taken into account when modelling cohesive sediment transport, either by using the calculated standard deviations for settling velocity, or by introducing a floc size (settling velocity) distribution in the transport model.