چكيده لاتين :
Introduction
A flood warning system consists of three basic
components; monitoring, forecasting, and decisionmaking.
To reduce flood damages by early flood
warrung, forecasting IS required which involves
uncertainties due to the height and liming of the floods.
Shortage of data or inaccurate model calibration may
cause false warning. Therefore, uncertainties associated
with forecasting are inevitable in real time decision
making. To achieve a more reliable warning. a longer
duration of data collection is required; however this
could not guarantee a long enough lead-time. For
logical and real time decision making as well as
performance evaluation, it is necessary to study and
quantify the uncertainties and rcliabilities of the flood
warning system.
Objective
The purpose of this paper is to apply a systematic
approach of reliability assessment and lead-time
calculation (Norouzi, et al., 20(7) for the flood warning
system of the Madarsou Basin installed in 2005. This
basin is located in the northeast of Iran. In this
methodology two terms are identified: i) Relative
Operation Characteristics (ROC) which is a relation
between probability of detection and probability of
false warning for a floodplain zone and its
transformation, ii) Performance Trade-off
Characteristics (PTC) which is a relation between
expected number of detections and expected number of
false warnings per year for a zone. For finding the
optimal point in calculation of the lead-time, the tradeoff
between reliability and lead-time is substantial. Methodology
To clarify the performance of the system, three models
of monitoring. forecasting, and decision making are
introduced. Associated parameters are defined as
follows:
Triggering indicator (7) and flood indicator (6) are
binary indicators representing the monitoring model.
The dual parameters of diagnosticity and reliability for
the software and hardware of the monitoring
component are also essential for the verification.
Forecasting model is denoted by; ho: flood stage, h:
height of the actual flood crest. and s: height of the
forecasted flood crest. The decision-making model is
on the other hand formulated by two binary indicators
(i.e, w: warning indicator and (): zone flood indicator),
s·: warning thercshold, and y: elevation of the
floodplain (v ?:hll ).
A given binary indicator vector (T, w, e, El) may have
four performance statuses defined as follows; I)
Missed Flood: M ~ (w~018~1, e~I), 2) False Warning:
F~(w~ 118~0, T~ 1),3)Oetection:O~(w~lle~1.
e~I), and 4) Quiet: Q ~ (w ~ 018 ~ 0, T ~ I). These
statuses are observable in the sense that one could
count their Occurrences over a period of time. In the
limit, this count would givc rise to conditional
probabilities of incorrect system performance of P(M)
and P(F) and correct system pcrfonnance of prO) and
P(Q).
Within each threshold value of sʹ , the probability of
detection and the probability of false warning are
calculable The illustration of pm) versus P(F),
obtained by varying s" from S/I to 00, is called the
ROC . To provide a tangible and desirable space for system
evaluation the probabilistic space should be
transformed to the corresponding expected number of
status, that is ND and NF. The plot of ND versus NF is
cailed the PTC.
Hence. the reliability assessment of a flood warning
system is possible as long as the performance
probabilities, P(D) and P(F), and their transformations,
ND and NF. are accessible. A correct decision must
come up to a remarkable lead-time.The reliability
assessment should however be considered along with
the lead-time.
The interval time between the warning and the flood
occurrence in a specified zone elevation, (y) is called
potential lead-time (PLT, (),(y)) and should be specified
for each zone elevation. Since, PLT is not constant for
an elevation in unsteady flow, in a rough and ready
estimation the expected value of ).(y) is the best
evaluation for PLT.
Consequently, the trade-off discussion among the three
terms of ROC, PTC, and PLT could represent the
functionality of the system deliberately, so that it
identifies and justifies the optimum point for each
elevation (y), in which oot only the performance of the
system is more reliable, but also the provided lead-time
is extended enough.
Results and Discussion
The methodology was applied to the Madarsou flood
warning system in northwestern parts of Iran. Due 10
the lack of basic data, the data was synthetically
generated by suitable models. Therefore, the task of
each component was defined separately and was
clustered in an assumed real-time space. In this case,
one control cross section, three vulnerable areas, three
forecasting times of 30, 90, and 180 minutes for
forecasting the flood crest height, two forecaster
triggering stages (i.e. S,~1.5m and S2~2.7m), and three
warning thresholds (i.e. 3m, 3.5m and 4m) were
considered. In the forecasting process, Clarck and
Muskingham-Cunge models were employed for basin
simulation and flood routing, respectively.
For the reliability assessment, the Weibull distribution
was fitted to data to represent corresponding
uncertainties (Krzysztofowicz, et al., 1994). By
programming in MATLAB P(D) and P(F) and also the
expected values of N(D) and N(F) were calculated and
graphs of ROC and PTC were plotted for the assumed
thresholds and forecasting times. Meanwhile, the PLT was estimated for the cited
vulnerable areas, considering flood traveling time.
Table (l) shows results of the lead-time calculations of
Dasht village, one of the vulnerable zones, for S, and
S2 and three warning thresholds.
Table 1- Potential Lead-Time calculation for a
vulnerable zone
Potential Lead-Time (hr)
Location 5, S,
3.0m 3.5m 4.0m 3.0m 3.5rn 4.0m
Dasht
village 17.00 18.91 10.83 7.71 IUS 14.97
Results showed that, the longest potential lead-time is
related to the 30 minute forecasting time, regardless of
the warning thresholds. The Reliability-Lead-time
trade-off discussion demonstrated that for each
operating point (i.e. the adjusted point on ROC or PTC
curve) for the higher trigger stages the potential leadtime
decreases by increasing the system reliability.
The results of the 30 minute forecasting time in
Madorsou showed that by increasing the lead-time up
to 9.28 hours, the number of missed flood increases
from 15.10 to 17.78.
Conclusion
To achieve an efficient and functional flood warning
system, assessment of reliability is essential especially
for recently installed systems. In this paper, an
appropriate model for reliability assessment was
introduced and applied to the Madarsou flood warning
system. The approach can properly identify the
pcrfonnance of the system, whether mature or new, and
help decision makers or planners. Integration of the
achieved results and the operational data will provide a
powerful data-base which can promote the functionality
of the flood warning system.
