PROBABILITY ESTIMATION OF SUPPLY RELIABILITY ASSESSMENTS.

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PROBABILITY ESTIMATION OF SUPPLY RELIABILITY
ASSESSMENTS.

• Ohanes Santourdjian, Donka Shopova
• Institute of Water Problems,
• Bulgarian Academy of Sciences

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Water supply reliability is necessary to be
considered when there is possibility for water
shortages, when the demand can exceed the
available supply.It is assessed in the cases of
dimensioning the capacity of a new water resource
system or checking the degree of supply
security of the existing water users. .
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The supply reliability is basically defined by
two indicators - reliability by volume. It is
measured by the percentage of the expected
satisfaction of the demand by volume and -
reliability by years which is the percentage of
the years with fully covered demand during the
planned future period of the water resource
system operation.
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These indicators are calculated by direct
comparison of the volumes of the predicted
possible inflow (run-off), limiting the supply,
to the volumes of the planned demand. This is
done for equal intervals, mostly months, during a
long enough time period. This calculation is
known as water resource balances (WRB)
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The essence of the problem consists in the
strongly variable character of the run-off. The
simulation of the expected future run-off can be
done by series of its measured realizations
during possibly longer periods in the past. These
periods can practically amount to several scores
of years. The run off can also be simulated by
generated by models series of 1000 and more
years, on the basis of the measured series.
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These series are used for computation of the
reliability indicators. They are equal to the
ratio of the supplied to the demanded water
volumes or of the years with full supply to the
whole number of the years in the period of
run-off simulation series.
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However it is very important to point out that
these values are calculated as average values
over long periods, (the period of run-off
simulation) supposed to contain all run-off
variations. They are valid for that period. They
can be 100 fulfilled if only the planned
operation period of the system coincides with the
run-off simulation period.
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But the planned operation period is always much
shorter than the period for run-off simulation.
In fact within its limits only some of the
run-off variations can take place. Depending on
their character the reliability indicators can
assume a wide range of values, higher or lower
than the average value. Then obviously the
average value is an indefinite indicator for
measuring the reliability of the supply.
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To improve the supply reliability assessment it
is proposed the following method.The supply
reliability indicators to be calculated for
periods only as long as the period of water
supply planning. But the water resource of that
period should be simulated by multitude of time
series with the same length and including all
possible realizations of the run-off.
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A basic assumption making the method possible, is
that these short series should be parts of the
long series of the run-off simulation period at
the site. They are excerpts from it, and belong
to the same totality of the run-off realizations.
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In calculation should be considered all possible
different excerpts with the length of the
planning period, that can be extracted from the
run-off simulation period. Their number is
IMN1, where M is the members number in the
run-off simulation period and N is the same for
the excerpts. If for example M1000 years and
N15 then I 986. This could be achieved if the
excerpts are arranged with maximum density, with
one member shift.
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The reliability indicators must be calculated for
all run-off possible realizations in the planned
period. The obtained ltIgt number indicators are
arranged according to their values and graphics
of their probability curves can be built.
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The method is illustrated by an example with a
water user from a multi-annual reservoir. There
are measured 50 years long monthly inflow series
- from 1926 to 1975. On their basis two modeled
1000 years long time series were generated.
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Calculated by the traditional method through
these series the supply reliability by volume is
between 100 to 99 and by years - 98 to 92The
planned time period for reliability estimation is
15 years. The measured series contain only 46,
while the generated ones - 986 possible 15 year
excerpts.
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CONCLUSIONSThe traditional method for supply
reliability evaluation is indefinite and not
enough informative for the decision maker.
Instead of calculation of one, single reliability
indicator value considering the all variations of
the source, with the proposed method are
calculated all possible for the planned
estimation period values.
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This enables achieving full knowledge of the
possible supply reliability values. The test
results show the consistence of the method.