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publications > scientific investigations report > water flow and nutrient flux from five estuarine rivers > computation of discharge > index-velocity relation

Computation of Discharge

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Computation of Discharge
- Cross-Sectional Relation
> Index-Velocity Relation
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Index-Velocity Relation

Linear index-to-mean velocity regression models (index-velocity relations) were developed for each station relating index velocity to mean velocity computed from measured discharge. Mean velocity was computed by dividing the measured discharges by the cross-sectional area (determined from the cross-sectional area equations) of the channel for the mid-time of the discharge measurement. Index velocities were then plotted against the mean channel velocities and analyzed using multiple-linear regression techniques. The independent variables used in the multiple-linear regression analysis were index velocity, index-velocity squared, and water level; whereas the dependent variable was mean-channel velocity (mean velocity). Index velocity was the only significant linear predictor of mean velocity for each station. However, the index-velocity relations had significant changes in slope for positive (downstream) and negative (upstream) velocities at the Broad, Harney, and Shark River stations. Index-to-mean velocity relation plots for the five stations are shown in figures 3A-E. The index-to-mean velocity equations and basic statistics are shown in table 3. Instantaneous discharge for each river station was computed by multiplying estimated mean velocity (using the index-to-mean velocity relation equations) by area (using the water level to cross-sectional river area relation equations).

index velocity to mean velocity regression relations for Lostmans Creek index velocity to mean velocity regression relations for Broad River
index velocity to mean velocity regression relations for Harney River index velocity to mean velocity regression relations for Shark River
index velocity to mean velocity regression relations for North River
Figure 3. Index velocity to mean velocity regression relations for Lostmans Creek, Broad River, Harney River, Shark River, and North River stations. [click on images above for larger versions]

Table 3. Index velocity regression equations and discharge error estimates using standard error estimate method.

[All equations are for mean velocity in the stream, in feet per second. R2, correlation coefficient; ft/s, feet per second; ft2, square feet; ft3/s, cubic feet per second; Vm, mean velocity in feet per second; Vi, measured index velocity in feet per second; S.E.E., standard error of the estimate]
Station Number of discharge measurements Equation R2 Standard error of the estimate
(ft/s)		 Median crosssectional area
(ft2)		 Instantaneous discharge error for median cross-sectional area
(ft3/s)
(S.E.E. * median area)
Lostmans Creek 58 Vm = 1.031 Vi + 0.092 0.92 0.23 927 213
Broad River
Positive velocity 86 Vm = 0.8182 Vi + 0.012 0.98 0.05 1,379 65
Negative velocity 47 Vm = 0.919 Vi - 0.001 0.98 0.04 1,379 54
Harney River
Positive velocity 53 Vm = 0.9388 Vi - 0.02 0.98 0.06 4,521 254
Negative velocity 71 Vm = 0.827 Vi + 0.005 0.96 0.07 4,521 326
Shark River
Positive velocity 89 Vm = 0.6926 Vi - 0.054 0.94 0.10 4,362 453
Negative velocity 47 Vm = 0.7564 Vi + 0.0007 0.94 0.08 4,362 331
North River 131 Vm = 0.7017 Vi - 0.04181 0.60 0.17 1,143 193

< Computation of Discharge | Discharge Error >


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