methodology for determining the optimum return period of design for

Transcription

E-proceedings of the 36th IAHR World Congress
28 June – 3 July, 2015, The Hague, the Netherlands
METHODOLOGY FOR DETERMINING THE OPTIMUM RETURN PERIOD OF DESIGN FOR FLOOD
MITIGATION, CASE: BOGOTA RIVER
(1)
JUAN PABLO QUIJANO , MARIO DIAZGRANADOS
(1)
Universidad de los Andes,Bogotá,Colombia,
[email protected]
(2)
Universidad de los Andes,Bogotá,Colombia,
[email protected]
(2)
ABSTRACT
Damage and flooding events derive in the need of cost-effective investments for prevention and control. Computer
programs have been turned in useful tools to support decision making. This study proposes a methodology applied in
Bogota River upper watershed to find an optimal return period for design of levees in river banks, using several of these
tools. A register of land uses was made determining urban, agricultural, animal breeding, flower crops, educational and
other zones. At the same time, unit costs, quantities and assets inventory were established for each lot in the study area.
Flood footprints, water height, velocities and levee height for different return periods flows (2, 3, 5, 10, 20, 50, 100, 200,
500 and 1000 years) were determined. Flooded areas were crossed with land use and damage costs were calculated.
Since the construction of any levee does not eliminate completely all the risk of damage, expected cost of damage were
estimated. Based on the levee heights and lengths, construction costs were generated as the sum of workforce, materials
and machinery costs. Finally, total costs were established (expected cost plus levee construction costs for each return
period) whose minimum was the optimal return period for design. This methodology was applied in two scenarios in
Bogota River upper watershed and it resulted in an optimal return period of 150 years for the current scenario and 125 for
the prospective scenario.
Keywords: Flood, economic analysis, optimum return period.
1.
INTRODUCTION
Civilizations and people traditionally have been established around or near water bodies due to dependence for
consumption, agriculture, recreation and sanitation. However, it means exposure to hazards such as floods, tidal waves
and tsunamis, aggravated by the apparent increase in frequency and magnitude as a consequence of the climate change
(Sanders, 2007).
In the second half of 2010 and the first half of 2011, a rainy season caused flooding in the central and northern part of
Colombia. The Presidency of Colombia estimated that during the first four months of 2011 had allocated $ 9 million USD
for flood mitigation, plus $ 4 million USD spent on remedial work only in the north part of the country (Presidencia de la
República, 2011).
Flood events mentioned above indicate the need of hydrological detailed studies, as well as better water resources
management. This refers to planning, management and mitigation of extreme events that result in cost-effective
interventions and reductions in cost damages (Torres, Sepulveda, Stull, & Holloway, 2011).
Addressing the hydrological threat from computational tools has been a way to cope this problematic. One challenge has
been to engage technical and economic analysis to select optimal solutions. In this study a methodology for obtaining
optimal return period for design (Tr*) was proposed. Tr* is understood as that which generates the lowest aggregate cost
of expected damages and construction costs; in this case is limited to the building of land dikes.
The case study is located south of Bogotá River upper basin in the municipality of Chía (see Figure 1), where the floods in
2010 and 2011 left flooded roads, 862 hectares were affected by losses of breeding animal and crops. Universities,
residential, sub urban areas, agricultural and pastoral areas are some of the different land uses concentrated in the area.
1
E-proceedings of the 36th IAHR World Congress,
Figure 1. Bogota Basin and Study Area.
2.
METODOLOGY
The proposed methodology includes hydrological, hydraulic and economic modeling including a calibration process. Two
scenarios were stipulated: 1. Current and 2. Prospective. The first scenario recreates the condition at time of the study in
which the area had some levees principally in private properties. The second presents a scenario which includes the
hydraulic adequacy of the river (dredging and widening of the cross section) beginning with an initial condition without any
levee protection. The methodology is summarized in Figure 2.
Figure 2. Optimum return period flow diagram.
The hydrologic modeling involved a frequency analysis of flow and volumes. Synthetic hydrographs were generated from
the analysis of historical events (return periods of 2, 3, 5, 10, 20, 50, 100, 200, 500 and 1000 years). The hydraulic
modeling was based on bathymetry of the river and contour lines of the area, from it was possible to create a digital
elevation model.
River2D and HEC-RAS, two free software were used. With the hydraulic analysis flood maps, levels, speed and height of
the levees were generated. All these results were exported to a Geographic Information System (GIS).Calibration and
validation of hydraulic models were made by comparing the model results with a historical flood event of 2011 and
watermarks (from field visits) in structures present in the study site.
2
The economic modeling was divided into two segments: 1. Estimation of damage cost 2. Assessment of levees
construction costs. Both were made with programs in MATLAB.
2.1 Estimation of damage cost
First the inventory of land uses was performed by tracing them through aerial photographs in GIS software. Different land
uses were established: agriculture, animal breading areas, suburban blocks, schools, universities, clubs, shopping
centers, flower warehouses, roads, and special uses.
From data collected in field and secondary information, each zone was incorporated with different data depending on the
land use (land costs, stratum numbers of livestock or agricultural products, etc.), allowing the creation of a database with
relevant information to cost estimation.
With the flood footprints; obtained from the hydraulic model, and land uses, the land uses inside the flooded area were
obtained (see Figure 3).
Figure 3. Flow diagram to obtain land uses inside the flood footprint.
Subsequently the main costs for each land use including animal breading, agriculture, suburban (residential), floriculture,
highways and others were established for each return period (Tr). First, from equations [1], [2], [3] and [4] animal breading
costs were estimated.
(#
=
,
)
,
[1]
$
∗
,
,
(#
=(
)
∗
,
∗
ℎ
,
(
(#
=
)
=
,
)
$
( ))
∗
∗
[2]
,
,
(
∗
+
)
,
+
ℎ
[3]
$
∗
∗
,
[4]
ℎ
:
(2, 3, 5, 10, 20, 50, 100, 200, 500
ℎ
)
1000
1…
For areas where land use is focused on agriculture, damage costs were determined with equations [5], [6] and [7] where
are described the crops lost cost and the land overhauling.
,
ℎ
(
=
=
)
(
,
∗
)
,
∗
(
[5]
$
∗
,
)(
,
$
[6]
)
[7]
=
,
+
ℎ
ℎ
,
:
3
(2, 3, 5, 10, 20, 50, 100, 200, 500
ℎ
)
1000
1…
The residential land use, specifically the damage caused to residential properties and suburban blocks, was also
considered according to the equation [8] where the cost depends on the flooded area, the unit cost of the land and a
vulnerability factor.
(
=
)
[8]
$
∗
,
∗
,
,
ℎ
:
(2, 3, 5, 10, 20, 50, 100, 200, 500
ℎ
)
1000
1…
Since one of the main economic activities in the study area is the floriculture, damage to these areas were considered by
the equation [12] whose terms are determined with equations [9], [10] and [11].
,
(
=
ℎ
,
)
,
∗
,
(
=
,
)
(
=
(
∗
,
)
,
[9]
$
∗
,
$
)(
,
[10]
)
[11]
$
∗
,
,
[12]
=
+
ℎ
ℎ
+
:
(2, 3, 5, 10, 20, 50, 100, 200, 500
ℎ
1000
)
1…
Moreover, the cost associated with flooded roads was considered by the equation [15] which includes the costs for
additional travel time (equation [13]) and disruption costs (equation [14]).
,
(ℎ
=
∗
ℎ
(
)
,
ℎ
)
∗
,
ℎ
,
$
∗
[13]
,
,
[14]
=
∗
,
=
,
ℎ
[15]
+
,
:
(2, 3, 5, 10, 20, 50, 100, 200, 500
ℎ
1000
)
1…
Any damage caused to schools, universities, clubs and shopping centers were considered through the unit cost of the
affected land (equation [16]). Finally, the opportunity cost is determined by the equation [17].
ℎ
,
(
=
)
,
$
∗
[16]
∗
,
,
=
∗
(
30
)
,
(
∗
)
,
[17]
,
,
ℎ
:
(2, 3, 5, 10, 20, 50, 100, 200, 500
4
$
∗
1000
)
ℎ
1…
Thus, within the flooded area each type of land use was identified and the corresponding equation of cost was applied
(see Figure 4). Speeds and average water levels in each site were taken into account to establish vulnerability factors
(speeds above 1 m / s and 1 meter higher altitudes increase the factor).
Figure 4. Example to obtain the agriculture cots for a return period of 100 years.
The total damage cost was determined by adding the different costs of damage using Equation [18]:
[18]
=
+
+
+
+
ℎ
:
ℎ
+
ℎ
ℎ
+
:
(2, 3, 5, 10, 20, 50, 100, 200, 500
1000
)
The above process was carried out for each return periods (Tr) and thus a damage curve was obtained (see Figure 5 and
Figure 6).
Figure 5. Procedure to obtain damage cost for a return period of 100 years.
5
Figure 6. Procedure to determine the damage curve.
Once the damage curve was obtained, expected damages were generated. The expected costs for a return period “X” are
the result of the sum of all costs associated with higher return period of “X” and each one multiplied by the probability of
occurrence of the event. This was done from the integration of the cost damage curve. The principal assumption used was
that the return period of the flood event is equal to the return period of damage (Oliveri & Santoro, 2000).
2.2 Construction cost estimation
Construction costs of levees were calculated from three variables: workforce, machinery and material (Equation [19]).
[19]
=
+
ℎ
+
(2, 3, 5, 10, 20, 50, 100, 200, 500
1000
)
Construction costs were determined, for each return period (2, 3, 5, 10, 20, 50, 100, 200, 500 and 1000), depending on
the length, height and time required for construction. In other words, for each flood footprint, the levees to prevent overflow
were determined and their construction costs were calculated (see Figure 7). Higher return periods imply the need to build
higher levees which increases construction costs.
Figure 7. Procedure to obtain construction cost for a return period of 100 years.
Finally, adding construction costs and expected damage costs, total costs are obtained, whose minimum corresponds to
the optimum return period for design (Tr*).
6
3.
RESULTS
Flow values, minimum, maximum and average volumes of a typical hydrograph were obtained with hydrological frequency
analysis for different return periods. These synthetic hydrographs (see Figure 8) were used in hydraulic models.
Figure 8.Sintetic hydrogram for different return periods (Tr).
From hydraulic modeling, flood footprints, speed and water level for each return period were obtained in a grid of 20x20
meters (see Figure 11 and Figure 13). Validation was conducted from a March 2011 event. In Figure 9 a comparison
between the simulated results of HEC-RAS and historic event (red line) is observed. It can be seen that they were similar
for extensions and flood levels allowing the execution of different scenarios.
Figure 9. Real and simulated event.
The digitization of each land use ended with a georeferenced map (Figure 10) where each polygon have a database
containing information of unit costs and principals features inventories of the area.
7
Figure 10. Land uses in the study area.
3.1 Current Scenario
Flood footprints for each of return periods are shown in Figure 11. As the return period increases, larger or deeper flooding
is generated, which leads to a more severe damage.
After applying the methodology described above it was determined that the optimal return period design (T r*) for this case
is 150 years (Figure 12). This means, from an economic point of view, it would be advisable to build the levees in the area
with an elevation that will prevent flooding for flows with return periods of 150 years.
Figure 11. Flood footprint – Current Scenario.
8
Figure 12. Cost vs return period – Current Scenario
3.2 Prospective Scenario
Similarly, for the prospective scenario flood footprint (Figure 13), expected damages curve and construction cost curve
were found. Figure 14 shows that the minimum of the total cost curve corresponds to an optimal return period of 125
years.
Figure 13. Flood footprint – Prospective Scenario.
9
Figure 14. Cost vs return period – Prospective Scenario
4.
CONCLUSIONS
The flood management has been characterized by the allocation of levees in specific sites with no economic analysis of
the area. This leads to transfer the problem to neighboring or downstream, that is why the use of technical and economic
watershed analysis is justified. The methodology presented in this work to determine the optimum return period leads to
an optimum from an economic point of view. The results showed reasonable optimal return periods that are within the
recommended in the literature and technical manuals, but with the advantage of having a technical and economic basis.
In the “current scenario” the optimum return period was 150 years, whereas in the “prospective scenario” was 125 years.
The difference between these two was that in the second a higher hydraulic capacity of the river is given from dredging
and widening of the cross section, requiring lower elevations of levees. However these costs would be necessary to add to
the costs of the hydraulic alteration.
Finally, it was noted that it is necessary to take into account economic and social factors in the area before designing
levees, in order to reduce damage costs and achieve optimal from an economic point of view.
ACKNOWLEDGMENTS
Asocolflores, CAR, Alcaldía de Chía, FEDEGAN, EUCO Ltda.
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methodology for determining the optimum return period of design for

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