dc.description.abstract | In this study, two simple linear catchment models
were used to model the rainfall-runoff characteristics
over Yala catchment.
The first model was based on the response function.
In this model a linear stochastic process for the rainfall runoff
system which yields the wiener-Hopf integral
equation was assumed. The method of maximum likelihood
was then used to compute optimum response functions.
The average response function together with the computed
areal rainfall were finally used to estimate stream flow
during the verification period.
In the second method, a multivariate autoregressive
model was used in which linear transfer functions of
different orders were fitted to the daily areal rainfall and
streamflow data. The optimum autoregressive model was
again used to estimate discharge during the verification
period.
The results from the two approaches were lastly
compared statistically.
Prior to fitting the models, the statistical
characteristics of the computed daily areal rainfall
and daily discharge series were investigated through
time series analysis. The characteristics of the
auto-correlation, cross-correlation, spectral and
cross-spectral functions were examined.
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Yala river basin is located in drainage
area one in western Kenya. The study was carried out
in this drainage basin using daily rainfall and discharge
records for nine years (1968 to 1976). The first seven
years were used for calibration of the models, while
the last two years were used for verification of the
skill of the fitted models. The calendar year was divided
into two seasons namely the long and short rain seasons •
.
The models were fitted for both seasons.
Results from spectral analysis, indicated periods
of 2 - 4 days, 5 - 7 days and 8 - 10 days in both rainfall
and discharge records. The results from the cross correlation
and coherence analyses showed significant
correlations between,time lags of 2 - 6 days with peaks
at a lag of 3 days during the first rain season and
a lag of 4 days during the-second rain season.
"
The response functions had peaks at a constant
time lag of 3 days during the first rain season and
-
4 days during t]1e second rain season.
The results from the fitted autoregressive models
indicated that the autoregressive models with four rainfall
and two discharge lag terms fitted the discharge- data
best.
It was noted that although both models could
not adequately estimate the extreme discharge values,
the response function model was better in real time
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forecasting. This model however, was poor in giving the
actual estimates of the observed discharge. On the other
hand, the autoregressive models gave good estimates of the
magnitudes of the discharges. The peak discharge values
were, however, shifted in some cases. It was therefore
suggested that the response function models which gave good
estimates of the time of occurrence of the discharge peaks
would be the best models for the Yala river basin for real
time forecasting. | en |