Do you have hysteresis effects in your data, i.e. could it be that concentrations measured during the "rising limb" of a flood peak behave differently from concentrations during the "falling limb" ?

You could have a look at publications dealing with (i) curve fitting or (ii) hysteresis effects, for example:

Crawford, C.G., 1991. Estimation of suspended-sediment rating curves and mean suspended-sediment loads. Journal of Hydrology 129, 331-348.

or

Girolamo, A.M. de, Pappagallo, G., Lo Porto, A., 2015. Temporal variability of suspended sediment transport and rating curves in a Mediterranean river basin. The Celone (SE Italy). Catena 128, 135-143.

Cheers

Tobias

Often a power law is fitted to the data using linear regression on log transformed values of flow and concentration. This results in a fit that matches the geometric mean (GM) rather than the arithmetric mean (AM). Any scatter in the residuals will result in the model under-estimating the AM as the GM is always less than the AM in this situation.

The over-estimation of the low concentrations (at low flows) can be the result of the data not following a power law. In some situations, the power law at the lowest flows can give concentrations well below any that have been observed. This is because the power law will be zero if the flow is zero. This doesn't match what will actually happen, and shows that if the flows get low enough, the power law is a poor approximation to the relationship between concentration and flow. I have often used a power law plus a constant (i.e. [s]=aQb+c). While this fits the data better, it requires use of a non-linear fitting algorithm rather than linear regression, and some people try to avoid use of non-linear algorithms because they require use of a iterative optimisation approach rather than the straight forward calculation for linear regression.

You should always plot the data to see what the relationship looks like. I would also suggest that you also plot the residuals of your fit to see whether there is any systematic pattern that your fit is not capturing.

This was studied by my colleague Margareta Jansson in this study: http://erlingsson.com/authorship/Cachi/Regulated_Rivers.pdf 

As you can see, she divided the data in classes to avoid the bias. Hope it helps.