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D - i D. MATHEMATICAL MODEL AND SIMULATION

D. MATHEMATICAL MODEL AND SIMULATION · 2005. 6. 29. · Please refer to MOUSE Pipe Flow Reference Manual for details. D - 3 The general steps to carry out simulation by MOUSE are:

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  • D - i

    D. MATHEMATICAL MODEL AND SIMULATION

  • D - ii

    TABLE OF CONTENTS

    Page

    D.1 Objective of Model Development ........................................................................... D - 1

    D.2 Selection of Software .............................................................................................. D - 1

    D.3 General Steps of Simulation by MOUSE................................................................ D - 1

    D.4 Cases of Simulation by MOUSE............................................................................. D - 3

    D.5 Model Development for Existing Condition ........................................................... D - 5

    D.6 Model Calibration ................................................................................................... D - 8

    D.7 Simulation Results ................................................................................................ D - 16

    LIST OF TABLES

    Page

    Table D.4.1 Hydrodynamic Simulation Cases .................................................................... D - 4

    Table D.5.1 Summary of Features of Model Development ................................................ D - 5

    Table D.6.1 Runoff Calculation Parameters for North Manila (1/2) ................................ D - 10

    Table D.6.1 Runoff Calculation Parameters for North Manila (2/2) ................................ D - 11

    Table D.6.2 Runoff Calculation Parameters for South Manila (1/2) ................................ D - 12

    Table D.6.2 Runoff Calculation Parameters for South Manila (2/2) ................................ D - 13

    Table D.6.3 Start and Stop Levels and Capacities of Pump Stations................................ D - 15

    Table D.6.4 Pump Capacity Curves .................................................................................. D - 15

    Table D.7.1 Simulated Inundated Areas by Depth and Duration for North Manila.......... D - 18

    Table D.7.2 Simulated Inundated Areas by Depth and Duration for South Manila.......... D - 19

    LIST OF FIGURES

    Page

    Figure D.3.1 Schematic Diagram of Simulation by MOUSE ............................................ D - 2

    Figure D.5.1 Hydrodynamic Simulation Network for North Manila ................................. D - 6

    Figure D.5.2 Hydrodynamic Simulation Network for South Manila ................................. D - 7

    Figure D.6.1 Water Levels during 1999 Inundation at Pump Stations

    along Pasig River ........................................................................................ D - 14

    Figure D.7.1 Inundation Map of Depths and Durations for Different Cases (1/7)........... D - 20

    Figure D.7.1 Inundation Map of Depths and Durations for Different Cases (2/7)........... D - 21

    Figure D.7.1 Inundation Map of Depths and Durations for Different Cases (3/7)........... D - 22

    Figure D.7.1 Inundation Map of Depths and Durations for Different Cases (4/7)........... D - 23

    Figure D.7.1 Inundation Map of Depths and Durations for Different Cases (5/7)........... D - 24

    Figure D.7.1 Inundation Map of Depths and Durations for Different Cases (6/7)........... D - 25

    Figure D.7.1 Inundation Map of Depths and Durations for Different Cases (7/7)........... D - 26

    Figure D.7.2 Inundation Characteristics of the Study Area

    from Simulation Result (1 of 2) .................................................................. D - 27

    Figure D.7.2 Inundation Characteristics of the Study Area

    from Simulation Result (2 of 2) .................................................................. D - 28

  • D - iii

    Figure D.7.3 Longitudinal Profile of Maximum Water Level along

    Blumentritt Interceptor ................................................................................ D - 29

    Figure D.7.4 Longitudinal Profile of Maximum Water Level along

    Estero de Tripa de Gallina........................................................................... D - 30

  • D - 1

    D.1 OBJECTIVE OF MODEL DEVELOPMENT

    The study area comprises a complex network of interconnected esteros, drainage mains, laterals,

    and connecting pipes. In addition, hydraulic facilities like thrash screens, gates, reservoirs and

    especially pump stations connected by esteros and drainage mains make the flow condition

    highly unpredictable during inundation. To analyze the highly dynamic behavior of the

    interconnected drainage system of the study area, comprehensive hydrodynamic models for

    north and south drainage systems have been developed. The main objectives of the model

    development are:

    - to evaluate the existing capacity of the drainage system;

    - to evaluate the performance of the drainage system under design condition (different

    alternatives/scenarios such as with and without project condition) and

    - to prepare inundation maps for different scenarios and return periods.

    D.2 SELECTION OF SOFTWARE

    There are two sets of software widely used for hydrodynamic simulation of unsteady

    one-dimensional flow, namely:

    - For one-dimensional unsteady river flow simulation of non-urbanized area: MIKE 11

    (requires license) developed by Danish Hydraulic Institute (DHI) of Denmark and

    HEC-RAS (free) developed by Hydraulic Engineering Center (HEC) of U.S. Army Corps

    of Engineers.

    - For one-dimensional unsteady sewer flow simulation of urbanized area: MOUSE (requires

    license) developed by DHI and SWMM (free) developed by Environmental Protection

    Agency (EPA) of U.S.A.

    HEC-RAS and MIKE 11 are mainly for simulation of free surface flow and are not so suitable

    for simulation of pressurized pipe flow. SWMM still lack a user-friendly graphical user

    interface. Both HEC-RAS and SWMM have only the hydrodynamic part and for hydrologic

    (runoff) part, some other software like HEC-HMS (free) developed by HEC of U.S. Army

    Corps of Engineers has to be used. Also, MIKE 11, HEC-RAS and SWMM lack automatic

    inclusion of different hydraulic functions such as pumps and regulators. All these make

    difficult to apply these software for hydrodynamic simulation of the complex drainage system

    of the study area. Finally, MOUSE of DHI has been selected as the hydrodynamic modeling

    software for this study due to the following advantages/characteristics of MOUSE:

    - Simulates fully dynamic one-dimensional unsteady free surface and pressurized pipe flow.

    - Have automatic functions for various hydraulic facilities like pump, gate, valve etc.

    - Integrates runoff and hydrodynamic model in one unit.

    - Simulates sewer and open channel network of any complexity as well as flow over road.

    - Have user-friendly graphical user interface (GUI) to develop and run the model and view

    model results.

    D.3 GENERAL STEPS OF SIMULATION BY MOUSE

    Schematic diagram of simulation by MOUSE is shown in Figure D.3.1. MOSUE applies

    implicit finite difference method to solve St. Venant’s fully dynamic wave equation using

    Double-Sweep algorithm. Please refer to MOUSE Pipe Flow Reference Manual for details.

  • D - 3

    The general steps to carry out simulation by MOUSE are:

    - Construction of model network consisting of nodes (manholes, estero junctions etc.) and

    links connecting two nodes (esteros, drainage mains, roads etc.).

    - Setting up boundary conditions (tide level at Manila Bay, water level along Pasig River,

    pump and gate operation rule etc.).

    - Specifying inflow from upstream sub-basins and lateral inflow from intermediate

    sub-basins.

    - Adding supplementary data (elevation-storage relation etc.).

    - Specifying hydraulic parameters (roughness, time steps).

    - Carrying out simulation (water level, discharge, flood depth etc. are the model output).

    - Viewing and interpretation of simulation results by MIKE View.

    D.4 CASES OF SIMULATION BY MOUSE

    The Study went through the following five stages (or cases) while carrying out simulation by

    MOUSE:

    - Model Calibration: Simulation network without project condition has been developed

    during this stage. Existing esteros, drainage mains, hydraulic facilities / structures etc.

    have been used to set up the model. In addition, main roads have been added to

    incorporate flow connectivity and storage effect. Runoff analysis and hydrodynamic

    simulation under existing condition has been carried out during this stage. Runoff

    analysis has been carried out using divisions of reach-basins delineated based on existing

    drainage network, time of concentration computed based on existing drainage condition

    and runoff coefficient estimated under existing landuse condition. The developed model

    has been calibrated against August 1999 inundation. For calibration, inundation maps for

    both depth and duration have been used. The calibrated parameters were roughness of

    road which acts as flood plain, time of concentration and inundation storage from the

    uppermost catchments.

    - Sensitivity Analysis: After calibrating the model, simulations under existing condition as

    well as for dredged condition, with and without channel improvement works and also with

    and without pump stations have been carried out to understand the effect of tide, dredging,

    channel improvements, pump operation etc.

    - Alternative Study: Simulation network has been reconstructed during this stage with

    project condition based on proposed drainage system and facilities improvement plans for

    different alternatives. Divisions of sub-basins based on alternative plans, time of

    concentration based on improved drainage condition and runoff coefficient under future

    landuse condition has been taken into account for runoff analysis.

    - Scenario Simulation: Simulation has been carried out with and without project condition

    under different design rainfall events. As for rainfall events, 2, 3, 5, 10, 20 and 30 years

    return period have been used. For with project condition, proposed alternative plan has

    been applied.

    Table D.4.1 lists all the simulation cases. In total, 57 cases have been simulated: 26 for North

    Manila (Case E-4 = Case D-1 and Case S-4 = Case A-1) and 31 for South Manila (Case E-4 =

    Case D-1 and Case S-4 = Case A-2).

  • Comment

    Estero & Other Improvement Reach Basin Pump Rainfall Tide or Landuse

    Main Case Sub-Case ID Run Drainage Main Works Water Level

    Calibration Calibration C C-1 Existing - Existing Existing August-99 August-99Existing

    (2003)Model Calibration

    P-1 Existing

    P-2 Fully dredged

    D-1 Existing

    D-2

    D-3 Fully implemented Proposed

    Alternative-1 A-1

    Aviles

    increased,

    UriUri pump

    added

    Alternative-2 A-2 Existing

    E-1 Design 2-yr

    E-2 Design 3-yr

    E-3 Design 5-yr

    E-4 Design 10-yr

    E-5 Design 20-yr

    E-6 Design 30-yr

    M-1 Design 2-yr

    M-2 Design 3-yr

    M-3 Design 5-yr

    M-4 Design 10-yr

    M-5 Design 20-yr

    M-6 Design 30-yr

    F-1 Design 2-yr

    F-2 Design 3-yr

    F-3 Design 5-yr

    F-4 Design 10-yr

    F-5 Design 20-yr

    F-6 Design 30-yr

    Comment

    Estero & Other Improvement Reach Basin Pump Libertad Maricaban Rainfall Tide or Landuse

    Main Case Sub-Case ID Run Drainage Main Works Pond Diversion Water Level

    Calibration Calibration C C-1 Existing No Existing Existing No No August-99 August-99Existing

    (2003)Model Calibration

    T-1 0-hr Lag

    T-2 1-hr Lag

    T-3 2-hr Lag

    T-4 3-hr Lag

    P-1 Existing

    P-2 Fully dredged

    D-1 Existing No No

    D-2 No No

    D-3 No Yes

    D-4 Fully implemented Proposed Yes

    Alternative-1 A-1Gallina

    increasedYes No

    Alternative-2 A-2 Existing Yes Yes

    E-1 Design 2-yr

    E-2 Design 3-yr

    E-3 Design 5-yr

    E-4 Design 10-yr

    E-5 Design 20-yr

    E-6 Design 30-yr

    M-1 Design 2-yr

    M-2 Design 3-yr

    M-3 Design 5-yr

    M-4 Design 10-yr

    M-5 Design 20-yr

    M-6 Design 30-yr

    F-1 Design 2-yr

    F-2 Design 3-yr

    F-3 Design 5-yr

    F-4 Design 10-yr

    F-5 Design 20-yr

    F-6 Design 30-yr

    Existing

    Existing

    Proposed

    Proposed

    Proposed

    Existing

    ExistingNo

    Existing

    Existing

    Proposed

    Proposed

    ProposedFully

    implemented

    Yes

    Existing

    No

    Existing

    Fully

    dredgedFuture

    Model Cases Model Network

    South Manila

    Boundary Condition

    Design

    Aviles

    increased,

    UriUri pump

    added (Same as

    Alternative A-1)

    E

    Design

    Design

    For damage

    analysis without

    project condition

    For damage

    analysis with full

    project

    implementation (as

    of M/P menu)

    Future

    Future

    Table D.4.1 Hydrodynamic Simulation Cases

    Effect of pump

    Fully

    implemented

    Boundary Condition

    Alternative Study A

    Pump Effect

    Existing

    Model Cases Model Network

    Fully

    dredged

    Sampaloc

    Interceptor

    Simulation

    Sensitivity

    Analyses

    -

    P No

    Channel

    Improvement

    Effect

    D Existing

    No

    Effect of

    improvement

    works

    No FutureDesign 10-yr Design

    Design 10-yrNo Alternative

    selection

    No operation Design FutureDesign 10-yrNo

    Simulation

    Sensitivity

    Analyses

    Tide Effect T

    Pump Effect P

    Channel

    Improvement

    Effect

    D

    Design 10-yrExisting

    (2003)

    Determine Lag

    time between

    design rainfall and

    tide peak

    Existing No Existing No

    Future Effect of pumpNo No operation No NoExisting

    Design 10-yr Design

    Design 10-yr Design

    Future

    Effect of

    improvement

    works

    Fully

    dredged

    Alternative Study AFully

    dredged

    Fully

    implementedDesign 10-yr Design Future

    Existing E Existing

    Selected

    AlternativeM

    Fully

    dredged

    Alternative

    selection

    For damage

    analysis without

    project condition

    No

    Fully

    implemented

    No

    Yes

    Yes

    (Same as

    Alternative A-

    2)

    Existing No

    No

    Aviles increased No

    Scenario

    Simulation

    North Manila

    Design Future

    For damage

    analysis with full

    project

    implementation (as

    of M/P menu)

    Design FutureNo

    Existing

    Existing

    Selected

    Alternative

    Partially

    dredged

    Partially

    implemented

    Scenario

    Simulation

    Fully

    dredged

    No

    Selected

    AlternativeM

    Design Future

    For damage

    analysis with

    partial project

    implementation (as

    of F/S menu)

    Selected

    AlternativeF

    Partially

    dredgedPartially implemented Existing Design

    F

    Future

    For damage

    analysis with

    partial project

    implementation (as

    of F/S menu)

    No No

    D - 4

  • D - 5

    D.5 MODEL DEVELOPMENT FOR EXISTING CONDITION

    Schematic diagrams of model networks under existing condition for south and north drainage

    areas (Case C-1 and other cases with existing estero and drainage mains) are shown in Figure

    D.5.1 and Figure D.5.2, respectively. There are slight differences in model networks for

    different cases as listed in Table D.4.1. Summary of features of simulation setup for south and

    north drainage areas is presented in Table D.5.1. Simulation model has been set up for total

    areas of 28.39 and 40.76 km2 covering 98% and 93% for North and South Manila, respectively.

    Total area covered by hydrodynamic simulation is 69.15 km2, which is about 95% of the total

    Study area. Total length of simulation network for north and south drainage areas includes

    24.12 and 35.05 km of estero and 17.15 and 20.79 km of drainage main, respectively, and roads

    with connections. Total number of cross-sections for north and south drainage areas are 181

    (49 from JICA Study Team (2004) and 132 from SEDLMM (2000)) and 217 (132 from JICA

    Study Team (2004) and 85 from SEDLMM (2000)), respectively. Total number of nodes for

    north and south drainage areas is 389 and 360, respectively. Total number of pumps for north

    and south drainage areas is 8 and 9, respectively (with equal numbers of gates).

    Table D.5.1 Summary of Features of Model Development

    Feature Attribute Drainage Area

    North South Total

    Nodes (maximum)

    (varies by case)

    Manholes along drainage mains,

    junctions of estero and drainage

    mains, nodes on roads (number of

    nodes)

    389 360 749

    Links (maximum)

    (varies by case)

    Esteros, drainage mains and roads

    (number of links) 616 469 1,085

    Estero (length in m) 24,117 35,054 59,171

    Estero (number of reaches) 18 17 35

    Drainage main

    (length in m) 17,154 20,788 37,942

    Estero and Drainage

    Mains (maximum)

    (varies by case)

    Drainage main (number) 18 18 36

    9 m wide (length in m) 13,835 8,768 22,603

    16 m wide (length in m) 12,399 10,594 22,993 Roads (maximum)

    (varies by case) 20 m wide (length in m) 14,378 26,401 40,779

    JICA Study Team (2004) survey

    (number) 49 132 181 Cross-Sections

    (maximum)

    (varies by case) SEDLMM (2000) survey

    (number) 132 85 217

    Pumping stations (number) 8 9 17 Hydraulic Facilities

    (maximum)

    (varies by case) Gates (number) 8 9 17

    Area (ha) 2,839 4,076 6,915 Reach-Basins

    (maximum)

    (varies by case) Catchment (number) 51 55 106

  • D - 8

    D.6 MODEL CALIBRATION

    The developed simulation models for both North and South Manila have been calibrated against

    1999 inundation depth and duration surveyed by SEDLMM (2000). The 1999 inundation has

    a return period of 10 years or less. After developing model networks for North and South

    Manila under existing condition, model calibration has been carried out through the process of

    runoff analysis and hydrodynamic simulation. The main model parameters were time of

    concentration of the catchments’ contributing flow and storage in the flood plain or reach basins.

    However, to keep the calibration process simple, time of concentration has been estimated

    separately instead of calibrating it inside the MOUSE model. During the estimation of time of

    concentration by reach basin, runoff analysis has been carried out repeatedly with different flow

    velocity and the peak runoff by each reach basin has been checked so that the runoff analysis

    produces reasonable specific runoff for all the reach basins. The estimated time of

    concentration (called lag time in MOUSE runoff model) by reach basins as well as other basin

    parameters like runoff coefficient, areal reduction factor etc. were inputted directly in the runoff

    model of MOUSE. It should be noted that flow velocity in channels was estimated based on

    the existing condition, which reflects the effects of deposition of garbage and sediment, for

    calibration case. As for the storage in the reach basins, road network, as detailed as possible,

    has been carefully integrated into the model through repeated simulation of the hydrodynamic

    model. In a similar manner, after several runs of the hydrodynamic model of MOUSE,

    roughness coefficient of road has been selected as 0.10, which produces good agreement with

    1999 observed inundation maps. This means that roads in the present simulation model act as

    virtual floodplain channels that reflect the effects of buildings surrounding those on inundation

    flow. For catchments in the uppermost reaches of the esteros (2 in North Manila with reach

    basin ID RNE 02_03 and RNE 03_01 and 2 in South Manila with reach basin ID RSE 18_02

    and RSE 19_01) for which no road network has been set up, storages of those catchments have

    been included in the basin nodes of uppermost estero of those catchments as elevation-area data.

    Stage-storage relation of the above mentioned reach basins have been extracted using GIS

    database of contour and basin boundary.

    (1) Runoff Model

    Runoff model in MOUSE consists of loss model that defines loss due to infiltration and storages,

    and hydrograph model that defines the shape of runoff hydrograph. For the present study,

    Proportional Loss, or in other words Rational Method, has been applied as the loss model.

    Rational Method is almost standard for runoff analysis of urban area. Rational method has

    been applied extensively by previous studies due to less parameter and easiness in application

    with acceptable degree of accuracy. As for the shape of hydrograph, triangular unit

    hydrograph of the Unit Hydrograph Model (UHM) has been selected, which produces runoff

    hydrograph with peak runoff very close to peak runoff calculated by Rational method (a little bit

    less due to non-symmetric nature of triangular unit hydrograph applied by MOUSE UHM

    model).

    For ease of modeling, small sub-basins have been grouped into reach-basins, where a reach

    basin is defined as the catchment contributing flow to a reach or branch between two junctions

    of estero-drainage mains. In total, 106 reach basins or catchments have been inputted in the

    runoff model with 51 and 55 for North and South Manila, respectively. In the MOUSE runoff

    model, the runoff parameters were area (in ha), aerial reduction factor, runoff coefficient and lag

    time (in hour). Table D.6.1 and D.6.2 show the runoff parameters for both the existing and the

    proposed drainage schemes.

  • D - 9

    As for rainfall, hourly rainfall data at Port Area from August 1-6, 1999 (5 days) has been used.

    Due to absence of hourly (chart) rainfall data at Science Garden and no data at NAIA and

    Napindan, only Port Area rainfall has been used for runoff analysis. To include the effect of

    spatial distribution of rainfall, aerial reduction factor for each reach basin has been applied.

    (2) Boundary Condition

    Hourly tide level at Manila Bay and observed water level along the Pasig River during 1999

    inundation has been applied as dynamic boundary condition at the downstream mouths of

    esteros and drainage mains. Figure D.6.1 shows the observed water levels at different pump

    stations along the Pasig River. Rainfall at Port Area and tide at Manila Bay during 1999

    inundation are presented in the meteo-hydrology part. No return flow from the Pasig River

    through small outlets of drainage was taken into account in the simulation model, because of

    difficulty to estimate it and its uncertainty.

    (3) Pump and Gate

    There exist 7 large pumps in the North and 8 large pumps in the South Manila. Start and stop

    levels of each pump station along with design capacity is listed in Table D.6.2. Differential

    type pumps have been set up in the MOUSE model along with non-return valves at gate of each

    pump station. Capacity curve (dH-Q data) of each pump station has been calculated based on

    only available experimental data at Vitas pump station assuming that all the pump stations

    behave in a similar way. The capacity curve tables of the pump stations are presented in Table

    D.6.3.

    (4) Hydrodynamic Simulation

    Fully dynamic wave model has been applied for hydrodynamic simulation. Variable time step

    of 30 to 600 seconds with an increasing factor of 1.5 has been used since MOUSE automatically

    adjusts the time step to get the maximum optimum time step that produces stable simulation.

    MOUSE automatically calculates an initial water surface based on boundary condition applying

    non-uniform flow equation. Even though, at the onset of simulation, the initial water level

    might deviate from real or design condition, within a few time steps, the water levels at every

    point of the simulation network come close to real or design condition and no problem could be

    encountered with automatic adjustment of initial water level of MOUSE model.

    Manning’s roughness coefficient for esteros and drainage mains have been selected based on

    information of estero and drainage mains’ bed and side materials (from survey result), field visit,

    previous studies and FCSEC guidelines.

    Type of Manning’s Roughness Coefficient (n value)

    Channel Existing Condition Improved Condition

    Estero 0.030 0.025

    Drainage Main 0.018 0.015

    Road (Floodplain) 0.10 0.10

    Inflow points of runoff from the catchments to the simulation network (at nodes) have been

    specified based on topography, laterals, catchment shape, flow path etc.

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    0.4

    80

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    0.7

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    .78

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    0.8

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    .33

    11

    25

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    0.8

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    .08

    8.4

    51

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    .83

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    70

    .81

    59

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    73

    48

    0.2

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    .26

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    .35

    79

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    0.7

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    0.2

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    0.7

    53

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    0.8

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    0.6

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    .75

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    0.7

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    0.3

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    0.9

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    .14

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    08

    23

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    1.3

    00

    .93

    S0

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    SE

    18

    _0

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    .94

    29

    3.5

    00

    .98

    0.5

    60

    .65

    40

    34

    1.7

    52

    30

    91

    .75

    23

    09

    73

    40

    .85

    0.8

    5

    S0

    1S

    01

    _0

    1R

    SE

    19

    _0

    15

    .40

    54

    0.1

    20

    .96

    0.5

    30

    .56

    42

    49

    1.5

    02

    84

    21

    .50

    28

    42

    12

    20

    .82

    0.8

    2

    S0

    1S

    01

    _0

    3R

    SE

    20

    _0

    10

    .55

    54

    .95

    1.0

    00

    .64

    0.6

    41

    19

    61

    .04

    11

    52

    1.0

    41

    15

    29

    18

    0.5

    80

    .58

    Tab

    le D

    .6.2

    R

    un

    off

    Calc

    ula

    tio

    n P

    ara

    mete

    rs f

    or

    So

    uth

    Man

    ila (

    2/2

    )

    (Pro

    po

    sed

    Dra

    inag

    e S

    ch

    em

    e)

    Tim

    e o

    f C

    on

    . (L

    ag T

    ime)

    Are

    a

    Ru

    no

    ff C

    oef

    fici

    ent

    Rea

    ch B

    asin

    Pro

    po

    sed

    Ex

    isti

    ng

    D - 13

  • Sour

    ce:

    Com

    pile

    d da

    ta u

    sing

    raw

    dat

    a fr

    om p

    ump

    stat

    ions

    off

    ices Fig

    ure

    D.6

    .1

    Wat

    er L

    evel

    s d

    uri

    ng

    199

    9 In

    un

    dat

    ion

    at

    Pu

    mp

    Sta

    tio

    ns

    alo

    ng

    Pas

    ig R

    iver

    Val

    enci

    a P

    S

    10.5

    11.0

    11.5

    12.0

    12.5

    13.0 0

    7/31

    07/3

    108

    /01

    08/0

    108

    /02

    08/0

    208

    /03

    08/0

    308

    /04

    08/0

    408

    /05

    Tim

    e

    Water Level (EL. m)

    Esc

    olta

    PS

    10.5

    11.0

    11.5

    12.0 0

    7/31

    07/3

    108

    /01

    08/0

    108

    /02

    08/0

    208

    /03

    08/0

    308

    /04

    08/0

    408

    /05

    Tim

    e

    Water Level (EL. m)

    Avi

    les

    PS

    11.0

    11.5

    12.0

    12.5 0

    7/31

    07/3

    108

    /01

    08/0

    108

    /02

    08/0

    208

    /03

    08/0

    308

    /04

    08/0

    408

    /05

    Tim

    e

    Water Level (EL. m)

    Lib

    erta

    d P

    S

    10.5

    11.0

    11.5

    12.0 0

    7/31

    07/3

    108

    /01

    08/0

    108

    /02

    08/0

    208

    /03

    08/0

    308

    /04

    08/0

    408

    /05

    Tim

    e

    Water Level (EL. m)

    Bal

    ete

    PS

    10.5

    11.0

    11.5

    12.0

    12.5 0

    7/31

    07/3

    108

    /01

    08/0

    108

    /02

    08/