HEALTH AND SANITATION
where demand exceeds supply to determine the storage
capacity (Fewkes and Butler, 2000). The critical period
methods base the reservoir capacity on a single worst
critical period or a synthesized one (Ndiritu et al., 2011). yield before spillage (YBS) algorithm. The two release
rules were originally developed by Jenkins, et al.
(1978), but later further development was done by
Fewkes (2000).
BEHAVIOURAL ANALYSIS
The continuous simulation method (behavioural
analysis) uses a simple mass balance equation. This
approach is popular because it can be applied with
simple mathematical tools as spreadsheet applications
and incorporates seasonal changes with relative ease
(Raimondi and Becciu, 2014). The limitations of the
model are that: depending on the length of the annual
inflow data, storage size for high reliabilities cannot
be estimated (McMahon et al., 2007). Considering
stochastically generated annual streamflows, Pretto et al.
(1997) found that biases occur in the mean and higher
order quantiles of storage estimates before the estimated
storage size converges to a stationary value after a long
sequence (typically 1 000 years or more). The yield after spillage operating rule:
• Yt=min {Dt Vt−1
• Qt=min{Vt−1+Qt−Yt S−Qt
The yield before spillage operating rule is:
• Yt=min{Dt Vt−1+Qt
• Qt=min{Vt−1+Qt−Yt S
Where: Rt= Rainfall [m] during interval, t; Qt=
Rainwater run-off [m 3 ] during time interval, t; Mt=
Mains supply make-up [m 3 ] during time interval, t; Ot=
Overflow from store [m 3 ] during time interval, t; Vt=
Volume in store [m 3 ] during time interval, t; Yt= Yield
from store [m 3 ] during time interval, t; Dt= Demand
[m 3 ] during time interval, t; S= Store Capacity [m 3 ] and;
A= Roof Area [m 2 ].
Behavioural models simulate the operation of the
reservoir with respect to time by routing the simulated
mass flows through an algorithm which describes the
operation of the reservoir (Fewkes and Butler, 2000).
The input data, which is in time series format, is used
for the simulation of the mass flows through the model
and will be based upon a time interval of either a minute,
hour, day or month (Fewkes and Butler, 2000) — they
have found more preference (McMahon and Adeyole,
2005; Ndiritu et al., 2011a, Raimondi and Becciu, 2014),
because they represent the storage behaviour more
realistically than other methods and it can be adapted
with ease to model complex configuration and operating
rules (McMahon and Adeyole, 2005).
There are two releases rules mainly involved in
behavioural models, namely yield after spillage (YAS) or
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In the YBS rule, the water is supposed to be
abstracted for use before the inflow at each time step
and which leads to underestimation of the storage
volume that is needed. The opposite is the case
with the YAS, which is more conservative and then
is usually preferred (Raimondi and Becciu, 2014).
Fewkes and Butler (2000) found that a YAS model
using either hourly or daily input time series could be
used to predict system performance.
Continued on page 33 >>
The operation of the system is usually simulated over a
given period of time using a time step of a minute, hour
or month (Fewkes and Butler, 2000). Several models that
can be used for the design and modelling of the storage
tank have been developed (Fewkes and Butler, 2000; Su
et al. 2009; Ndiritu et al., 2011). The difference in the
models is the release rule which may be YAS or YBS as
explained later. Fewkes and Butler (2000) investigated
the accuracy of behavioural models using different time
steps with the YAS and YBS release rule for both small
and large storages. Each model run was one year; the
results of this preliminary analysis indicated that a YAS
model using either hourly or daily input time series could
be used to predict system performance. Some models
have been incorporated into software packages while
others operate in Excel.
31
Calculating rainfall is critical for determining storage capacities.
January 2019 Volume 25 I Number 1