Application of straight channel methods to meandering data

6.2.1 The methods

The methods used in this work are listed below. These are simple methods which are practical to apply by hand. The Lateral Distribution Method which was found to give good results for straight channels has not been included in this assessment since it is a computational model and the research programme put a high priority on hand calculation methods. The various composite roughness methods have not been included here since their performance against straight channel data was poor.

DCM Divided Channel Method, using vertical division lines which are

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included in the wetted perimeter of the main channel but omitted from the wetted perimeter of the floodplains. Main channel slope used for main channel flow.

SCM Single Channel Method, using main channel slope.

SSGM Sum of Segments Method. Main channel slope used for main channel segments.

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

Main channel slope used for main channel flow.

FCFAM Method developed by Ackers, based on Flood Channel Facility Phase A data. Main channel slope used for main channel flow.

HOR1 Divided Channel Method, using a horizontal division line at bankfull stage. Division line is included in floodplain wetted perimeter but not in main channel wetted perimeter. Floodplain slope used for main channel and floodplain flows.

HOR2 Divided Channel Method, using a horizontal division line at bankfull stage. Division line is included in floodplain and main channel wetted perimeters.

Floodplain slope used for main channel and floodplain flows.

HOR3 Divided Channel Method, using a horizontal division line at bankfull stage. Division line is included in floodplain wetted perimeter but not in main channel wetted perimeter. Main channel slope used for main channel flow.

HOR4 Divided Channel Method, using a horizontal division line at bankfull stage. Division line is included in floodplain and main channel wetted perimeters. Main channel slope used for main channel flow.

The two divided channel methods (DCM and DCM2); the single channel method (SCM); the sum of segments method (SSGM) and the FCFAM method (ACKM) were all applied as described above. These are the standard simple methods which could be used to calculate flows in compound channels. The various horizontal

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division line methods (HOR1, HOR2, HOR3, HOR4) are simplifications of the methods proposed by Toebes and Sooky (1967) and Smith (1977). The main channel and floodplains are considered to be split by a horizontal line at bankfull level. The region above the dividing line is included in the floodplain area when calculating the floodplain flow. The sinuosity of a meandering channel is the ratio of the curvilinear distance along the channel to the straight distance between the two points.

6.2.2 The data set

The SERC FCF Phase B stage-discharge test programme is summarized in Table 5.1 and the results of stage and discharge are presented in detail in Appendix 5. Of this data series numbers B32, B33, B46 and B48 have been excluded from this analysis for the following reasons.

B32, B46 Floodplain roughened with rows of isolated breeze blocks, special methods must be used to account for the head losses due to these blocks.

B33 Floodplain only partially roughened. The roughness zones were limited to the ’meander belt’, creating two distinct roughness regions on the floodplains. The methods described above are suitable for floodplains which are homogeneously roughened.

B48 Floodplains are totally blocked by breeze block walls which run from the inner bend apices to the outer edge of the floodplain. This simulates the case were development has occurred over the whole floodplain. Again the simple methods used here are not suitable for this geometry.

The series B21, B26, B31, B34, B39, B43 and B47 from Phase B of the FCF were all analyzed using the methods described above. In total 107 data points were used in this analysis. The full details of the experiments are given in Section 5.2. The bed friction terms for the various tests were calculated using a modified smooth law for the smooth cases and the Ackers rod roughness method for the roughened cases.

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6.2.3 Results

The mean errors and standard deviations in the mean errors for the various methods are listed in Table 6.1. The results differed considerably depending whether the floodplains were roughened or not and so mean errors are given over the smooth data, the roughened data and over all the smooth and rough data. Table 6.1 shows that for the whole data set the mean errors for the various methods vary from 7.3%

to 70.1%. All the methods over-predict discharge by significant amounts. The corresponding standard deviations vary between 16.8% and 56.7% showing that the errors vary by very large margins about the mean values.

It is worth looking more closely at the results averaged over the smooth and rough data sets. The mean error for the fourth horizontal division line method (HOR4) taken over all the data is 7.3% and so this method would appear to give the best results. However when the mean error is calculated over the smooth and rough data sets the mean errors are 19.5% and -19.8% respectively. Thus the relatively low mean error achieved by considering the whole data set is actually the result of large positive errors for the smooth cases and large negative errors for the rough cases.

This wide band of errors is highlighted by the large values of the standard deviations.

The results discussed above show that the simple methods developed for straight compound channels are likely to give rise to large errors in estimated discharges if applied to meandering compound channels. The range of errors to be expected will vary with the following parameters:

1 sinuosity

2 floodplain width / main channel width

3 floodplain roughness / main channel roughness 4 floodplain depth / main channel depth

For cases similar to the Phase B geometries considered, the errors in calculated discharges may be as large as 100%. Hence a different method is required to

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calculate the discharge in meandering compound channels.

The four methods based on a simple two way division with a horizontal line at bankfull stage appear to perform slightly better overall than the other methods. This suggests that horizontal divisions are most appropriate for meandering channels. In straight compound channels the best divisions are based on vertical divisions at the edges of the main channel.

Of the methods applied to the meandering laboratory data the horizontal division methods gave marginally more accurate predictions. In general straight channel methods are not appropriate for the analysis of meandering compound channels. This confirmed that the development of a new procedure for discharge estimation in meandering compound channels is worthwhile.