The methods

The methods detailed below were identified as appropriate for application to measured stage discharges in straight compound channels.

LDM Lateral Distribution Method with NEV = 0.16

DCM Divided Channel Method, using vertical division lines which are included in the wetted perimeter of the main channel but omitted from the wetted perimeter of the flood plains

SCM Single Channel Method, applying the bankfull main channel Manning’s n value to the whole compound channels

SCM2 Horton’s Composite Roughness Method SCM3 Lotter’s Composite Roughness Method

SCM4 Einstein and Banks Composite Roughness Method

SCM5 Krishnamurthy and Christensen Composite Roughness Method SSGM Sum of Segments Method

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DCM2 Divided Channel Method, using vertical division lines which are not included in the wetted perimeter of either the main channel or the flood plains

ACKM Ackers’ Method, based on Flood Channel Facility Phase A data. Main channel slope used for main channel flow.

These methods for calculating discharge in straight compound channels fall into four broad categories: divided channel methods; method of segments; composite roughness methods and more complex physically based methods. These methods have been applied to the various data sets available.

4.6.2 SERC FCF Phase A Total Discharge

The various composite roughness methods are not applicable to the SERC FCF, since the bed roughness terms are not approximated with Manning’s equation and the comparison was carried out with the single channel and divided channel methods only. Each method was applied to individual discharge observations and the error in predicted discharge calculated. The standard NEV value, 0.16, was used with the LDM.

Table 4.14 gives the mean errors and variances for each test series. All three methods are sensitive to channel geometry and give smaller errors as the floodplain widths are reduced. Both the LDM and the two divided channel methods tend to over predict flows while the SCM under predicts, as expected Ackers’ method performs the best overall on this data set. Figures 4.47 and 4.48 show the variation of error in the calculated flows with depth for the various methods.

At low floodplain depths the DCM gives approximately zero error which rises to between 10% and 15% at relative depths of about 0.15 as the depth increases further

f

the error drops back towards zero. The other divided channel method (DCM2) gives a very similar distribution of errors but displaced upwards by about 5%. The SCM

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gives much larger errors at low relative depths than either the DCM or DCM2.

Maximum errors of between -50% and -30% were found, with the wider floodplain cases giving the larger errors. As the depth increases the errors reduce, tending towards zero at relative depths of about 0.75. The hydraulic behaviour of compound channels at low floodplain depths is quite different from compact channels but at large depths the main channel becomes a minor local area of increased depth. The lateral velocity gradients, which generate considerable turbulence and flow resistance at low depths, are reduced and the flow starts to approach the compact channel state.

Ackers’ method was developed using this data and, not surprisingly, it gives the most consistently accurate results.

Overall the LDM performs slightly better than the DCM and significantly better than the SCM. Table 4.15 shows the mean errors and variances taken over the whole data set. On average the LDM gave errors of about 3.4% compared to the DCM with 5.0%, the DCM2 at 7.7%, the SCM at -13.7% and Ackers’ method at 0.3%. In terms of standard deviation the LDM and the two divided channel methods are similar with values close to 4.0%, the SCM is much worse at 14.0% and Ackers’ method had a standard deviation of 1.7%. For the rough floodplain case the LDM gave mean error and standard deviation of 3.7% and 5.5% respectively; the DCM 24.7% and 14.0%;

DCM2 12.1 and 11.8 and Ackers’ method was best at -2.0% and 3.8%.

It was also possible to calculate the errors in predicted depth using these data. The measured discharge values were used to interpolate between the discharges calculated at the measured stages to obtain the predicted depths for a given discharge. In general these results show similar distributions to the discharge results. Where a method over-predicts discharge then it under-predicts depth. The mean errors in calculated depth for each series are shown in Table 4.16 and Figures^The mean errors over the whole data set in Table 4.17. In general the errors in depth are considerably smaller than the equivalent errors in discharge, for example the LDM gives a mean error in discharge of 4.7% with a SD of 5.9% for series 1. The equivalent mean error and SD in terms of predicted depth are -1.3% and 1.1%. Thus the calculation of discharge in compound channels is far more sensitive to the method used than the

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calculation of stage or depth. This is probably due to the general shape of compound channel rating curves, which often have relatively mild slopes. It also explains why it has been possible to use and calibrate 1-D river models with a sufficient degree of accuracy even when a relatively crude method is used to calculate the conveyance of compound channels. These models are generally calibrated against water levels and the calculated water levels are relatively insensitive to the method used to compute the conveyances.

Figure 4.51 shows the mean errors and standard deviations in both the calculated discharges and depths for the SERC FCF Phase A data sets. Figure 4.52 shows a comparison between the measured and calculated distribution of flow between the main channel and floodplains for this data set. All the methods tend to over predict the proportion of flow in the main channel at low overbank depths but improve as depths become greater, except for Ackers’ method which gives good results at all levels. This is clearer in Figure 4.53 where the difference between calculated and measured (Qmc/Qtot) is plotted for the various methods. It is obvious that Ackers’

method predicts the main channel flow to within 1% consistently while the LDM gives it to about 2% and the two divided channel methods give good predictions at low overbank stages but get worse as the flow gets deeper.

It is not surprising that Ackers’ method and the LDM give good results when applied to this data set. Both of these methods have been developed based on (ACKM), or modified after application to (LDM), this data set. A far better test of these methods is to apply them to data sets not used in their derivation or development.