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E-1 As discussed in Chapter 7, there are two methods of defin- ing the angle (θ) of bend migration for a given period based on the migration of the bend centroid in previous periods. The first and simplest method is to use the direction defined by the previous period for the period being predicted. The second method uses the rate of change of the migration angle from the previous period to define the rate of change for the period being predicted (see Equation 7.4). The following is an estimation of the potential change in migration direction, based on the previous angle of bend migration for the exam- ple problem presented in Step 7 of Chapter 8. The migration angle θC is plotted relative to the arbitrary line as shown in Figure 8.13. The Period C angle of migra- tion (θC) relative to the arbitrary line will be the Period B angle (θB) plus the rate of movement of the bend centroid during Period B times the number of years in Period C (YC). The direction of the movement of the bend centroid during Period C, derived using Equation 7.4, is the following: As noted, if only one period is available, then one can assume that the migration direction does not change (θc = θB) or, using judgment, once can allow the future direction to deviate from θB. It would generally be assumed that the bend migration direction would tend more down valley with time. Comparison of Figures 8.13 and 8.14 with Figures E.1 and E.2 shows the difference in the predictions based on the two approaches. θ θ θ θC B A B C BY Y= â( )ï£«ï£ ï£¶ï£¸ ( )   + = ° â °( )ï£«ï£ ï£¶ï£¸ ( )   + ° = ° 46 13 5 26 30 46 83 5. . yr yr APPENDIX E PREDICTING CHANGE IN MIGRATION DIRECTION
E-2 Figure E.1. Prediction of change in migration direction for the period from 1998 to 2028 and the predicted position of the outer bank of the bend in 2028.
E-3 Figure E.2. Overlay of the predicted channel position in 2028 on the 1998 aerial photograph of the Sacramento River near Butte City, California, considering change in migration direction. Note the threat to the local levee.
