Developing Sediment Yield Prediction Equations for Small Catchments in Tanzania - Advances in Data, Methods, Models and Their Applications in Geoscience - page 254

Regression S tatistics
Multiple R 0.8081451

R Square 0.6530985

Adjusted R
Square

0.6442036

Standard
Error

0.1655968

Observations 41

ANOVA

df SS MS F Significance F

Regression 1 2.013449766 2.01345 73.423838 1.67761E-10

Residual 39 1.0694693 0.027422

Total 40 3.082919067

Coefficients Standard Error t Stat P-value Lower 95% Upper 95%

Intercept 2.7452 0.05577 49.21851 1.01E-36 2.632384636 2.858019

X variable 0.4313 0.04885 8.568771 1.678E-10 0.319783073 0.5174043

Table 3.2.1. Regression statistics in log scale for both dry and moderate zones data points

From Table 3.2.1 results we have, Log α = 2.7452 ± Standard Error, and thus α would range
from 439.20 to 632.27. And if you take the average you will get α = 556.16. Also the value of
β obtained as β = 0.4313± Standard Error. β would therefore range from 0.3824 to 0.4802
with the average value 0.4313. The resulting equation will look like (Equation 3.2)

SF = 556.2 A 0.4313 (3.2)
Where; SF= Sediment fill (m 3 /yr); A = Catchment area (km 2 ); α = constant; and β = scaling
exponent.
The corresponding graph of sediment fill-yield versus catchment area in dry and moderate
climatic zone (all regions analysed) is presented in Fig. 3.2.
One would note from Fig. 3.2 below that the developed equations satisfactorily predict the
sediment fill in small catchment at 95 % confidence interval. It is worth noting that a few of
the observed sediment fill-yield data points, for instance, for a catchment sizes of 2.8 and
16.5 km 2 from Tabora region (Table 2.2.2) plotted outside the prediction range ( i.e. , outlier).
The author is attributing it to uncertainty in field measurements. As reported in literature,
all techniques for estimating reservoir volume incorporate errors (Morris and Fan, 1998). An
estimated error of about ±30% in determining reservoir capacity volumes have been
reported in Morris and Fan (1998) by various workers. These discussions may suggest that
the error observed above could be explained by uncertainty in determining actual sediment
fill (reservoir sedimentation rate), (Ndomba, 2007). Such errors are also acknowledged by
Mulengera (2008). A set of sediment fill-yield prediction equations for various climatic zones