.96 to 1.00 with a median of .99. The only problem encountered 

 with the stage-discharge approach occurred in cross-sections 5, 

 6 and 7 of the Beaverhead subreach. These cross-sections tran- 

 sected an island and included a left and right channel. Be- 

 tween the highest and lowest calibration flows (34 3 and 255 cfs, 

 respectively) , the water surface elevations for these 3 cross- 

 sections decreased by .38 to .56 ft in the right channel and 

 only .22 to .24 ft in the left channel. The water surface ele- 

 vations for the right channel, which contained over 90% of the 

 flow, were used to calibrate the IFG-4 model. This was the 

 only situation in which the stage-discharge rating curve ap- 

 proach proved inadequate. ^- ~ .. ,.: -..,-• . 



The reliability of the velocity predictions as determined 

 by the correlation coefficients (r) for the velocity-discharge 

 relationships varied for each subreach (Table 27) . The median 

 r values by cross-section generally exceeded .90 for the 

 Madison #1, Madison #3, and Gallatin subreaches. The one 

 exception was cross-section #2 of the Madison #3 subreach in 

 which the median r value was .85. Correlations were poorest 

 for the Beaverhead subreach. In this subreach, median r values 

 by cross-section ranged from .46 to .915. Some of the poor 

 correlation can be attributed to the proximity of the calibra- 

 tion flows (255, 289, and 343 cfs). Morphological character- 

 istics of the subreach also appear to be a contributing factor. 

 Islands and gravel bars located at the head of the subreach 

 had an unexpected influence on the flow distribution and slope 

 of the water surface as the flows decreased. These influences 

 also produced many inverse velocity-discharge relationships. 

 Due to the problems encountered in the Beaverhead subreach, 

 the reliability of the velocity predictions obtained by ex- 

 trapolating beyond the highest and lowest calibration flows 

 is questionable. 



Based solely on an evaluation of correlation coefficients 

 (1^) , the rating curve approach for predicting velocities is 

 judged relatively poor for the Beaverhead subreach, fair for 

 the Big Hole subreach, and excellent for the remaining 

 three subreaches. 



The velocities generated by the IFG-4 model for the cali- 

 bration flows were also statistically compared by subreach to 

 the measured velocities using t-tests for paired data. This 

 analysis shows that the predicted velocities for all five 

 subreaches are significantly different (p <. 05) from the 

 measured velocities. Even though statistical differences 

 occurred, the magnitude of the bias of the predictions, as 

 measured by the differences between means for the IFG-4 pre- 

 dicted versus the measured velocities (Table 28) , does not ap- 

 pear large enough to have any practical significance in a real 

 world situation. The differences between means were all rela- 

 tively small, ranging from .051 to .161 ft/sec for the five 

 subreaches. ca . -ii* 



la a . v>Q • - -^ 



80 



i a 



