Developing Sediment Yield Prediction Equations for Small Catchments in Tanzania - Advances in Data, Methods, Models and Their Applications in Geoscience - page 251

made it difficult to establish a linear relationship between sediment load and river
discharge. Surveys of reservoirs/dams whose relevant technical maps were available were
done. Profiles available from old/design maps were compared with the new sounding.

2.3 Data analysis
Although the data collected are scarce ( i.e. , only 53 dams) but one could see that based on
climatic zonation about seventy percent (70%) of Tanzania land is represented. Besides, the
data coverage represents a wide range of dam and catchment physical characteristics viz.
catchment area 1 - 267 km 2 ; dam capacity at FSL, 0.02 - 35 Million m 3 (Table 2.3). The mean
values are 41.7 km 2 and 1.5 Million m 3 for catchment area and dam capacity, respectively.
Notwithstanding the high spatial variability of data as captured by high Coefficient of
variation (Cv), the data represent the population as demonstrated by low Standard Error of
the Mean (SEM).

Dam capacity at Full
Supply Level
(Million m 3 )
1. Lowest 1.20 0.02
2. Maximum 267.00 35.40
3. Mean 41.66 1.52
4. Standard Deviation (STD) 59.62 6.41
5. Coefficient of Variation, Cv (%) 143.12 422.76
6. Standard Error of the Mean, SEM 8.19 1.17
Table 2.3. Summary statistics of catchment size and dam capacity of data used in this study

Serial No. Statistics Catchment area

(km 2 )

2.4 Development of sediment yield-fill equations
Sediment yield-fill equations were developed by regression analysis approach. It should be
noted that if data on sediment yield-fill and catchment characteristics are available from
many sites, it may be possible to develop a regression relationship which describes the
sediment yield within the region as a function of independent variables such as catchment
area, slope, land use, and rainfall erosivity (Morris and Fan, 1998). The only independent
variable used for this study is the catchment area as it was readily available. This study
assumed the following: i) the sample is representative of the population for the inference
prediction; ii) the error is a random variable with a mean of zero conditional on the
explanatory variables; iii) the independent variables based on low standard error of the
mean (SEM) as presented in Table 2.3 were measured with no error; iv) the predictors are
linearly independent, i.e . it is not possible to express any predictor as a linear combination of
the others; v) the errors are uncorrelated, that is, the variance-covariance matrix of the errors
is diagonal and each non-zero element is the variance of the error; and vi) the variance of the
error is constant across observations (homoscedasticity). These are sufficient conditions for
the least-squares estimator to possess desirable properties, in particular, these assumptions
imply that the parameter estimates will be unbiased, consistent, and efficient in the class of
linear unbiased estimators. Besides, sediment yield is assumed as equal to sediment fill due
to the uncertainty involved in estimating trap efficiency of small dams in the study area. It
should be noted that previous researchers such as Mulengera (2008) adopted a similar