Page 364 - Soil and water contamination, 2nd edition

Patterns in surface water 351

In small urbanised catchments, the response of suspended sediment to runoff events may
be even more complex, as demonstrated by Lawler et al. (2006). In their study in the urban
headwaters of the river Tame, UK, counter-clockwise hysteresis responses of stream water
turbidity were observed during the majority of the runoff events, with the result that for a
given flow level, turbidity increased during the falling limb of the hydrograph (see Figure
18.7c-d). This is contrary to the response found in many other streams and rivers, including
urban ones, where suspended sediment concentrations typically peak during the rising
limb. In the Tame, increased turbidities during the falling limb co-occurred with elevated
ammonium concentrations, which suggests that overflow spills from combined sewer
overflows or wastewater treatment plants release sediments into the river. Such overflows

typically occur late in the hydrograph, during intense storm events when rainwater delivery
exceeds the storage capacity of the sewer system or wastewater treatment plant. Biofilms may
also play a role in the delayed sediment transport. The presence of biofilms may considerably
increase the critical shear stress for erosion of streambed sediments. Therefore, biofilms could
suppress bed and sewer sediment entrainment early in the hydrograph, but when the biofilm
breaks up due to the larger shear stresses around peak flow, more bed material is released
during the later part of the event (Lawler et al., 2006).
18.3.5 Concentration rating curve s

Because the hysteresis behaviour of the Q–C relationship is often not ambiguous, a long-
term Q–C relationship is frequently used for the prediction of unmeasured substance
concentrations from water discharge (Walling, 1977; Ferguson, 1986; Horowitz, 2002). Such
a long-term relationship is called a rating curve . Rating curves have especially been adopted
to estimate sediment concentrations or loads (e.g. Asselman, 1998; Horowitz, 2002). Usually
a concentration rating curve takes the form of a power function:

C a Q b (18.1)

-1
where C = the concentration of the substance under consideration (mg l ), Q = water
-1
3
discharge (m s ), and a and b are coefficients. Log transformation of Equation (18.1) yields
a linear equation:
log C log a b log Q (18.2)
where the logarithms are to base 10. Fitting a line to the log–log plot of C against Q using
least squares linear regression provides the values for a and b. However, predictions of C
using these coefficients are statistically biased because linear regression ensures that the mean
sample residual of log C equals zero. Using Equation (18.1) to predict C, however, yields
the geometric – not arithmetic – mean of the statistical distribution of C given a value for
Q. The geometric mean is always less than or equal to the arithmetic mean; to estimate the
arithmetic mean of C, Ferguson (1986) derived the following bias correction for Equation
(18.1):
C a Q b e . 2 65 s 2 (18.3)

2
where s = mean square error of the regression Equation (18.2), which is a measure of the
degree of scatter around the rating curve .
Figure 18.11 shows the uncorrected (Equation 18.1) and corrected (Equation 18.3)
sediment rating curve for sediment concentration measured in the river Rhine near Lobith,
the Netherlands. This figure shows that the scatter around the rating curve is considerable,

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